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Dieser Kreis heißt ",[771,805,551],{},".",[564,808,809,810,813,814,842,843,871,872,939],{},"Auch die ",[771,811,812],{},"Umkehrung"," gilt: Hat ein Dreieck bei ",[568,815,817,830],{"className":816},[571],[568,818,820],{"className":819},[575],[577,821,822],{"xmlns":579},[581,823,824,828],{},[584,825,826],{},[593,827,683],{},[604,829,683],{"encoding":606},[568,831,833],{"className":832,"ariaHidden":589},[611],[568,834,836,839],{"className":835},[615],[568,837],{"className":838,"style":695},[619],[568,840,683],{"className":841,"style":699},[624,652]," einen rechten Winkel, liegt ",[568,844,846,859],{"className":845},[571],[568,847,849],{"className":848},[575],[577,850,851],{"xmlns":579},[581,852,853,857],{},[584,854,855],{},[593,856,683],{},[604,858,683],{"encoding":606},[568,860,862],{"className":861,"ariaHidden":589},[611],[568,863,865,868],{"className":864},[615],[568,866],{"className":867,"style":695},[619],[568,869,683],{"className":870,"style":699},[624,652]," auf dem Kreis mit dem Durchmesser ",[568,873,875,896],{"className":874},[571],[568,876,878],{"className":877},[575],[577,879,880],{"xmlns":579},[581,881,882,894],{},[584,883,884],{},[587,885,886,892],{"accent":589},[584,887,888,890],{},[593,889,595],{},[593,891,598],{},[600,893,602],{"stretchy":589},[604,895,607],{"encoding":606},[568,897,899],{"className":898,"ariaHidden":589},[611],[568,900,902,905],{"className":901},[615],[568,903],{"className":904,"style":620},[619],[568,906,908],{"className":907},[624,625],[568,909,911],{"className":910},[629],[568,912,914],{"className":913},[633],[568,915,917,931],{"className":916,"style":620},[637],[568,918,919,922],{"style":640},[568,920],{"className":921,"style":645},[644],[568,923,925,928],{"className":924},[624],[568,926,595],{"className":927},[624,652],[568,929,598],{"className":930,"style":656},[624,652],[568,932,933,936],{"style":659},[568,934],{"className":935,"style":645},[644],[568,937],{"className":938,"style":667},[666],". Daraus folgt:",[941,942,943,947],"ul",{},[944,945,946],"li",{},"Der Mittelpunkt des Umkreises eines rechtwinkligen Dreiecks ist der Mittelpunkt der Hypotenuse.",[944,948,949],{},"Der Umkreisradius ist die halbe Hypotenuse.",[564,951,952],{},"Anwendung: rechtwinklige Dreiecke konstruieren und Tangenten von einem Punkt an einen Kreis zeichnen.",[559,954,956],{"id":955},"herleitung","Herleitung",[564,958,959,960,990,991,1058,1059,1127,1128,1196,1197,1265,1266,1304,1305,1196,1344,1383,1384,1416,1417,1445,1446,1474,1475,1416,1507,1535,1536,1564,1565,1621,1622,1660],{},"Sei ",[568,961,963,977],{"className":962},[571],[568,964,966],{"className":965},[575],[577,967,968],{"xmlns":579},[581,969,970,975],{},[584,971,972],{},[593,973,974],{},"M",[604,976,974],{"encoding":606},[568,978,980],{"className":979,"ariaHidden":589},[611],[568,981,983,986],{"className":982},[615],[568,984],{"className":985,"style":695},[619],[568,987,974],{"className":988,"style":989},[624,652],"margin-right:0.109em;"," der Mittelpunkt von ",[568,992,994,1015],{"className":993},[571],[568,995,997],{"className":996},[575],[577,998,999],{"xmlns":579},[581,1000,1001,1013],{},[584,1002,1003],{},[587,1004,1005,1011],{"accent":589},[584,1006,1007,1009],{},[593,1008,595],{},[593,1010,598],{},[600,1012,602],{"stretchy":589},[604,1014,607],{"encoding":606},[568,1016,1018],{"className":1017,"ariaHidden":589},[611],[568,1019,1021,1024],{"className":1020},[615],[568,1022],{"className":1023,"style":620},[619],[568,1025,1027],{"className":1026},[624,625],[568,1028,1030],{"className":1029},[629],[568,1031,1033],{"className":1032},[633],[568,1034,1036,1050],{"className":1035,"style":620},[637],[568,1037,1038,1041],{"style":640},[568,1039],{"className":1040,"style":645},[644],[568,1042,1044,1047],{"className":1043},[624],[568,1045,595],{"className":1046},[624,652],[568,1048,598],{"className":1049,"style":656},[624,652],[568,1051,1052,1055],{"style":659},[568,1053],{"className":1054,"style":645},[644],[568,1056],{"className":1057,"style":667},[666],". Die Strecken ",[568,1060,1062,1084],{"className":1061},[571],[568,1063,1065],{"className":1064},[575],[577,1066,1067],{"xmlns":579},[581,1068,1069,1081],{},[584,1070,1071],{},[587,1072,1073,1079],{"accent":589},[584,1074,1075,1077],{},[593,1076,974],{},[593,1078,595],{},[600,1080,602],{"stretchy":589},[604,1082,1083],{"encoding":606},"\\overline{MA}",[568,1085,1087],{"className":1086,"ariaHidden":589},[611],[568,1088,1090,1093],{"className":1089},[615],[568,1091],{"className":1092,"style":620},[619],[568,1094,1096],{"className":1095},[624,625],[568,1097,1099],{"className":1098},[629],[568,1100,1102],{"className":1101},[633],[568,1103,1105,1119],{"className":1104,"style":620},[637],[568,1106,1107,1110],{"style":640},[568,1108],{"className":1109,"style":645},[644],[568,1111,1113,1116],{"className":1112},[624],[568,1114,974],{"className":1115,"style":989},[624,652],[568,1117,595],{"className":1118},[624,652],[568,1120,1121,1124],{"style":659},[568,1122],{"className":1123,"style":645},[644],[568,1125],{"className":1126,"style":667},[666],", ",[568,1129,1131,1153],{"className":1130},[571],[568,1132,1134],{"className":1133},[575],[577,1135,1136],{"xmlns":579},[581,1137,1138,1150],{},[584,1139,1140],{},[587,1141,1142,1148],{"accent":589},[584,1143,1144,1146],{},[593,1145,974],{},[593,1147,598],{},[600,1149,602],{"stretchy":589},[604,1151,1152],{"encoding":606},"\\overline{MB}",[568,1154,1156],{"className":1155,"ariaHidden":589},[611],[568,1157,1159,1162],{"className":1158},[615],[568,1160],{"className":1161,"style":620},[619],[568,1163,1165],{"className":1164},[624,625],[568,1166,1168],{"className":1167},[629],[568,1169,1171],{"className":1170},[633],[568,1172,1174,1188],{"className":1173,"style":620},[637],[568,1175,1176,1179],{"style":640},[568,1177],{"className":1178,"style":645},[644],[568,1180,1182,1185],{"className":1181},[624],[568,1183,974],{"className":1184,"style":989},[624,652],[568,1186,598],{"className":1187,"style":656},[624,652],[568,1189,1190,1193],{"style":659},[568,1191],{"className":1192,"style":645},[644],[568,1194],{"className":1195,"style":667},[666]," und ",[568,1198,1200,1222],{"className":1199},[571],[568,1201,1203],{"className":1202},[575],[577,1204,1205],{"xmlns":579},[581,1206,1207,1219],{},[584,1208,1209],{},[587,1210,1211,1217],{"accent":589},[584,1212,1213,1215],{},[593,1214,974],{},[593,1216,683],{},[600,1218,602],{"stretchy":589},[604,1220,1221],{"encoding":606},"\\overline{MC}",[568,1223,1225],{"className":1224,"ariaHidden":589},[611],[568,1226,1228,1231],{"className":1227},[615],[568,1229],{"className":1230,"style":620},[619],[568,1232,1234],{"className":1233},[624,625],[568,1235,1237],{"className":1236},[629],[568,1238,1240],{"className":1239},[633],[568,1241,1243,1257],{"className":1242,"style":620},[637],[568,1244,1245,1248],{"style":640},[568,1246],{"className":1247,"style":645},[644],[568,1249,1251,1254],{"className":1250},[624],[568,1252,974],{"className":1253,"style":989},[624,652],[568,1255,683],{"className":1256,"style":699},[624,652],[568,1258,1259,1262],{"style":659},[568,1260],{"className":1261,"style":645},[644],[568,1263],{"className":1264,"style":667},[666]," sind alle Radien, also gleich lang. Damit zerfällt das Dreieck ",[568,1267,1269,1286],{"className":1268},[571],[568,1270,1272],{"className":1271},[575],[577,1273,1274],{"xmlns":579},[581,1275,1276,1284],{},[584,1277,1278,1280,1282],{},[593,1279,595],{},[593,1281,598],{},[593,1283,683],{},[604,1285,750],{"encoding":606},[568,1287,1289],{"className":1288,"ariaHidden":589},[611],[568,1290,1292,1295,1298,1301],{"className":1291},[615],[568,1293],{"className":1294,"style":695},[619],[568,1296,595],{"className":1297},[624,652],[568,1299,598],{"className":1300,"style":656},[624,652],[568,1302,683],{"className":1303,"style":699},[624,652]," in zwei gleichschenklige Dreiecke ",[568,1306,1308,1326],{"className":1307},[571],[568,1309,1311],{"className":1310},[575],[577,1312,1313],{"xmlns":579},[581,1314,1315,1323],{},[584,1316,1317,1319,1321],{},[593,1318,595],{},[593,1320,974],{},[593,1322,683],{},[604,1324,1325],{"encoding":606},"AMC",[568,1327,1329],{"className":1328,"ariaHidden":589},[611],[568,1330,1332,1335,1338,1341],{"className":1331},[615],[568,1333],{"className":1334,"style":695},[619],[568,1336,595],{"className":1337},[624,652],[568,1339,974],{"className":1340,"style":989},[624,652],[568,1342,683],{"className":1343,"style":699},[624,652],[568,1345,1347,1365],{"className":1346},[571],[568,1348,1350],{"className":1349},[575],[577,1351,1352],{"xmlns":579},[581,1353,1354,1362],{},[584,1355,1356,1358,1360],{},[593,1357,974],{},[593,1359,598],{},[593,1361,683],{},[604,1363,1364],{"encoding":606},"MBC",[568,1366,1368],{"className":1367,"ariaHidden":589},[611],[568,1369,1371,1374,1377,1380],{"className":1370},[615],[568,1372],{"className":1373,"style":695},[619],[568,1375,974],{"className":1376,"style":989},[624,652],[568,1378,598],{"className":1379,"style":656},[624,652],[568,1381,683],{"className":1382,"style":699},[624,652],". In ihnen sind die Basiswinkel gleich: Der Winkel ",[568,1385,1387,1402],{"className":1386},[571],[568,1388,1390],{"className":1389},[575],[577,1391,1392],{"xmlns":579},[581,1393,1394,1399],{},[584,1395,1396],{},[593,1397,1398],{},"α",[604,1400,1401],{"encoding":606},"\\alpha",[568,1403,1405],{"className":1404,"ariaHidden":589},[611],[568,1406,1408,1412],{"className":1407},[615],[568,1409],{"className":1410,"style":1411},[619],"height:0.4306em;",[568,1413,1398],{"className":1414,"style":1415},[624,652],"margin-right:0.0037em;"," bei ",[568,1418,1420,1433],{"className":1419},[571],[568,1421,1423],{"className":1422},[575],[577,1424,1425],{"xmlns":579},[581,1426,1427,1431],{},[584,1428,1429],{},[593,1430,595],{},[604,1432,595],{"encoding":606},[568,1434,1436],{"className":1435,"ariaHidden":589},[611],[568,1437,1439,1442],{"className":1438},[615],[568,1440],{"className":1441,"style":695},[619],[568,1443,595],{"className":1444},[624,652]," tritt auch bei ",[568,1447,1449,1462],{"className":1448},[571],[568,1450,1452],{"className":1451},[575],[577,1453,1454],{"xmlns":579},[581,1455,1456,1460],{},[584,1457,1458],{},[593,1459,683],{},[604,1461,683],{"encoding":606},[568,1463,1465],{"className":1464,"ariaHidden":589},[611],[568,1466,1468,1471],{"className":1467},[615],[568,1469],{"className":1470,"style":695},[619],[568,1472,683],{"className":1473,"style":699},[624,652]," auf, ebenso der Winkel ",[568,1476,1478,1493],{"className":1477},[571],[568,1479,1481],{"className":1480},[575],[577,1482,1483],{"xmlns":579},[581,1484,1485,1490],{},[584,1486,1487],{},[593,1488,1489],{},"β",[604,1491,1492],{"encoding":606},"\\beta",[568,1494,1496],{"className":1495,"ariaHidden":589},[611],[568,1497,1499,1503],{"className":1498},[615],[568,1500],{"className":1501,"style":1502},[619],"height:0.8889em;vertical-align:-0.1944em;",[568,1504,1489],{"className":1505,"style":1506},[624,652],"margin-right:0.0528em;",[568,1508,1510,1523],{"className":1509},[571],[568,1511,1513],{"className":1512},[575],[577,1514,1515],{"xmlns":579},[581,1516,1517,1521],{},[584,1518,1519],{},[593,1520,598],{},[604,1522,598],{"encoding":606},[568,1524,1526],{"className":1525,"ariaHidden":589},[611],[568,1527,1529,1532],{"className":1528},[615],[568,1530],{"className":1531,"style":695},[619],[568,1533,598],{"className":1534,"style":656},[624,652],". Der Winkel bei ",[568,1537,1539,1552],{"className":1538},[571],[568,1540,1542],{"className":1541},[575],[577,1543,1544],{"xmlns":579},[581,1545,1546,1550],{},[584,1547,1548],{},[593,1549,683],{},[604,1551,683],{"encoding":606},[568,1553,1555],{"className":1554,"ariaHidden":589},[611],[568,1556,1558,1561],{"className":1557},[615],[568,1559],{"className":1560,"style":695},[619],[568,1562,683],{"className":1563,"style":699},[624,652]," ist also ",[568,1566,1568,1587],{"className":1567},[571],[568,1569,1571],{"className":1570},[575],[577,1572,1573],{"xmlns":579},[581,1574,1575,1584],{},[584,1576,1577,1579,1582],{},[593,1578,1398],{},[600,1580,1581],{},"+",[593,1583,1489],{},[604,1585,1586],{"encoding":606},"\\alpha + \\beta",[568,1588,1590,1612],{"className":1589,"ariaHidden":589},[611],[568,1591,1593,1597,1600,1605,1609],{"className":1592},[615],[568,1594],{"className":1595,"style":1596},[619],"height:0.6667em;vertical-align:-0.0833em;",[568,1598,1398],{"className":1599,"style":1415},[624,652],[568,1601],{"className":1602,"style":1604},[1603],"mspace","margin-right:0.2222em;",[568,1606,1581],{"className":1607},[1608],"mbin",[568,1610],{"className":1611,"style":1604},[1603],[568,1613,1615,1618],{"className":1614},[615],[568,1616],{"className":1617,"style":1502},[619],[568,1619,1489],{"className":1620,"style":1506},[624,652],". Mit der Winkelsumme im Dreieck ",[568,1623,1625,1642],{"className":1624},[571],[568,1626,1628],{"className":1627},[575],[577,1629,1630],{"xmlns":579},[581,1631,1632,1640],{},[584,1633,1634,1636,1638],{},[593,1635,595],{},[593,1637,598],{},[593,1639,683],{},[604,1641,750],{"encoding":606},[568,1643,1645],{"className":1644,"ariaHidden":589},[611],[568,1646,1648,1651,1654,1657],{"className":1647},[615],[568,1649],{"className":1650,"style":695},[619],[568,1652,595],{"className":1653},[624,652],[568,1655,598],{"className":1656,"style":656},[624,652],[568,1658,683],{"className":1659,"style":699},[624,652],":",[568,1662,1665],{"className":1663},[1664],"katex-display",[568,1666,1668,1738],{"className":1667},[571],[568,1669,1671],{"className":1670},[575],[577,1672,1674],{"xmlns":579,"display":1673},"block",[581,1675,1676,1735],{},[584,1677,1678,1680,1682,1684,1686,1690,1692,1694,1696,1699,1702,1712,1715,1718,1720,1722,1724,1726,1728],{},[593,1679,1398],{},[600,1681,1581],{},[593,1683,1489],{},[600,1685,1581],{},[600,1687,1689],{"stretchy":1688},"false","(",[593,1691,1398],{},[600,1693,1581],{},[593,1695,1489],{},[600,1697,1698],{"stretchy":1688},")",[600,1700,1701],{},"=",[1703,1704,1705,1709],"msup",{},[1706,1707,1708],"mn",{},"180",[600,1710,1711],{},"∘",[1603,1713],{"width":1714},"1em",[600,1716,1717],{},"⇒",[1603,1719],{"width":1714},[593,1721,1398],{},[600,1723,1581],{},[593,1725,1489],{},[600,1727,1701],{},[1703,1729,1730,1733],{},[1706,1731,1732],{},"90",[600,1734,1711],{},[604,1736,1737],{"encoding":606},"\\alpha + \\beta + (\\alpha + \\beta) = 180^\\circ\n\\quad\\Rightarrow\\quad\n\\alpha + \\beta = 90^\\circ",[568,1739,1741,1759,1777,1800,1824,1888,1906,1924],{"className":1740,"ariaHidden":589},[611],[568,1742,1744,1747,1750,1753,1756],{"className":1743},[615],[568,1745],{"className":1746,"style":1596},[619],[568,1748,1398],{"className":1749,"style":1415},[624,652],[568,1751],{"className":1752,"style":1604},[1603],[568,1754,1581],{"className":1755},[1608],[568,1757],{"className":1758,"style":1604},[1603],[568,1760,1762,1765,1768,1771,1774],{"className":1761},[615],[568,1763],{"className":1764,"style":1502},[619],[568,1766,1489],{"className":1767,"style":1506},[624,652],[568,1769],{"className":1770,"style":1604},[1603],[568,1772,1581],{"className":1773},[1608],[568,1775],{"className":1776,"style":1604},[1603],[568,1778,1780,1784,1788,1791,1794,1797],{"className":1779},[615],[568,1781],{"className":1782,"style":1783},[619],"height:1em;vertical-align:-0.25em;",[568,1785,1689],{"className":1786},[1787],"mopen",[568,1789,1398],{"className":1790,"style":1415},[624,652],[568,1792],{"className":1793,"style":1604},[1603],[568,1795,1581],{"className":1796},[1608],[568,1798],{"className":1799,"style":1604},[1603],[568,1801,1803,1806,1809,1813,1817,1821],{"className":1802},[615],[568,1804],{"className":1805,"style":1783},[619],[568,1807,1489],{"className":1808,"style":1506},[624,652],[568,1810,1698],{"className":1811},[1812],"mclose",[568,1814],{"className":1815,"style":1816},[1603],"margin-right:0.2778em;",[568,1818,1701],{"className":1819},[1820],"mrel",[568,1822],{"className":1823,"style":1816},[1603],[568,1825,1827,1831,1835,1872,1876,1879,1882,1885],{"className":1826},[615],[568,1828],{"className":1829,"style":1830},[619],"height:0.7241em;",[568,1832,1834],{"className":1833},[624],"18",[568,1836,1838,1842],{"className":1837},[624],[568,1839,1841],{"className":1840},[624],"0",[568,1843,1846],{"className":1844},[1845],"msupsub",[568,1847,1849],{"className":1848},[629],[568,1850,1852],{"className":1851},[633],[568,1853,1855],{"className":1854,"style":1830},[637],[568,1856,1858,1862],{"style":1857},"top:-3.113em;margin-right:0.05em;",[568,1859],{"className":1860,"style":1861},[644],"height:2.7em;",[568,1863,1869],{"className":1864},[1865,1866,1867,1868],"sizing","reset-size6","size3","mtight",[568,1870,1711],{"className":1871},[1608,1868],[568,1873],{"className":1874,"style":1875},[1603],"margin-right:1em;",[568,1877],{"className":1878,"style":1816},[1603],[568,1880,1717],{"className":1881},[1820],[568,1883],{"className":1884,"style":1875},[1603],[568,1886],{"className":1887,"style":1816},[1603],[568,1889,1891,1894,1897,1900,1903],{"className":1890},[615],[568,1892],{"className":1893,"style":1596},[619],[568,1895,1398],{"className":1896,"style":1415},[624,652],[568,1898],{"className":1899,"style":1604},[1603],[568,1901,1581],{"className":1902},[1608],[568,1904],{"className":1905,"style":1604},[1603],[568,1907,1909,1912,1915,1918,1921],{"className":1908},[615],[568,1910],{"className":1911,"style":1502},[619],[568,1913,1489],{"className":1914,"style":1506},[624,652],[568,1916],{"className":1917,"style":1816},[1603],[568,1919,1701],{"className":1920},[1820],[568,1922],{"className":1923,"style":1816},[1603],[568,1925,1927,1930,1934],{"className":1926},[615],[568,1928],{"className":1929,"style":1830},[619],[568,1931,1933],{"className":1932},[624],"9",[568,1935,1937,1940],{"className":1936},[624],[568,1938,1841],{"className":1939},[624],[568,1941,1943],{"className":1942},[1845],[568,1944,1946],{"className":1945},[629],[568,1947,1949],{"className":1948},[633],[568,1950,1952],{"className":1951,"style":1830},[637],[568,1953,1954,1957],{"style":1857},[568,1955],{"className":1956,"style":1861},[644],[568,1958,1960],{"className":1959},[1865,1866,1867,1868],[568,1961,1711],{"className":1962},[1608,1868],[559,1964,1966],{"id":1965},"beispiele","Beispiele",[564,1968,1969,1970,2000,2001,2074,2075,2141,2142,2210,2211,2401,2402,1127,2713,1196,2996,3087,3088,1660],{},"Der Kreis um den Ursprung mit Radius ",[568,1971,1973,1987],{"className":1972},[571],[568,1974,1976],{"className":1975},[575],[577,1977,1978],{"xmlns":579},[581,1979,1980,1985],{},[584,1981,1982],{},[1706,1983,1984],{},"5",[604,1986,1984],{"encoding":606},[568,1988,1990],{"className":1989,"ariaHidden":589},[611],[568,1991,1993,1997],{"className":1992},[615],[568,1994],{"className":1995,"style":1996},[619],"height:0.6444em;",[568,1998,1984],{"className":1999},[624]," hat den Durchmesser von ",[568,2002,2004,2032],{"className":2003},[571],[568,2005,2007],{"className":2006},[575],[577,2008,2009],{"xmlns":579},[581,2010,2011,2029],{},[584,2012,2013,2015,2017,2020,2022,2025,2027],{},[593,2014,595],{},[600,2016,1689],{"stretchy":1688},[600,2018,2019],{},"−",[1706,2021,1984],{},[600,2023,2024],{},"∣",[1706,2026,1841],{},[600,2028,1698],{"stretchy":1688},[604,2030,2031],{"encoding":606},"A(-5 \\mid 0)",[568,2033,2035,2062],{"className":2034,"ariaHidden":589},[611],[568,2036,2038,2041,2044,2047,2050,2053,2056,2059],{"className":2037},[615],[568,2039],{"className":2040,"style":1783},[619],[568,2042,595],{"className":2043},[624,652],[568,2045,1689],{"className":2046},[1787],[568,2048,2019],{"className":2049},[624],[568,2051,1984],{"className":2052},[624],[568,2054],{"className":2055,"style":1816},[1603],[568,2057,2024],{"className":2058},[1820],[568,2060],{"className":2061,"style":1816},[1603],[568,2063,2065,2068,2071],{"className":2064},[615],[568,2066],{"className":2067,"style":1783},[619],[568,2069,1841],{"className":2070},[624],[568,2072,1698],{"className":2073},[1812]," nach ",[568,2076,2078,2102],{"className":2077},[571],[568,2079,2081],{"className":2080},[575],[577,2082,2083],{"xmlns":579},[581,2084,2085,2099],{},[584,2086,2087,2089,2091,2093,2095,2097],{},[593,2088,598],{},[600,2090,1689],{"stretchy":1688},[1706,2092,1984],{},[600,2094,2024],{},[1706,2096,1841],{},[600,2098,1698],{"stretchy":1688},[604,2100,2101],{"encoding":606},"B(5 \\mid 0)",[568,2103,2105,2129],{"className":2104,"ariaHidden":589},[611],[568,2106,2108,2111,2114,2117,2120,2123,2126],{"className":2107},[615],[568,2109],{"className":2110,"style":1783},[619],[568,2112,598],{"className":2113,"style":656},[624,652],[568,2115,1689],{"className":2116},[1787],[568,2118,1984],{"className":2119},[624],[568,2121],{"className":2122,"style":1816},[1603],[568,2124,2024],{"className":2125},[1820],[568,2127],{"className":2128,"style":1816},[1603],[568,2130,2132,2135,2138],{"className":2131},[615],[568,2133],{"className":2134,"style":1783},[619],[568,2136,1841],{"className":2137},[624],[568,2139,1698],{"className":2140},[1812],". Der Punkt ",[568,2143,2145,2171],{"className":2144},[571],[568,2146,2148],{"className":2147},[575],[577,2149,2150],{"xmlns":579},[581,2151,2152,2168],{},[584,2153,2154,2156,2158,2161,2163,2166],{},[593,2155,683],{},[600,2157,1689],{"stretchy":1688},[1706,2159,2160],{},"3",[600,2162,2024],{},[1706,2164,2165],{},"4",[600,2167,1698],{"stretchy":1688},[604,2169,2170],{"encoding":606},"C(3 \\mid 4)",[568,2172,2174,2198],{"className":2173,"ariaHidden":589},[611],[568,2175,2177,2180,2183,2186,2189,2192,2195],{"className":2176},[615],[568,2178],{"className":2179,"style":1783},[619],[568,2181,683],{"className":2182,"style":699},[624,652],[568,2184,1689],{"className":2185},[1787],[568,2187,2160],{"className":2188},[624],[568,2190],{"className":2191,"style":1816},[1603],[568,2193,2024],{"className":2194},[1820],[568,2196],{"className":2197,"style":1816},[1603],[568,2199,2201,2204,2207],{"className":2200},[615],[568,2202],{"className":2203,"style":1783},[619],[568,2205,2165],{"className":2206},[624],[568,2208,1698],{"className":2209},[1812]," liegt auf dem Kreis, denn ",[568,2212,2214,2254],{"className":2213},[571],[568,2215,2217],{"className":2216},[575],[577,2218,2219],{"xmlns":579},[581,2220,2221,2251],{},[584,2222,2223,2230,2232,2238,2240,2243,2245],{},[1703,2224,2225,2227],{},[1706,2226,2160],{},[1706,2228,2229],{},"2",[600,2231,1581],{},[1703,2233,2234,2236],{},[1706,2235,2165],{},[1706,2237,2229],{},[600,2239,1701],{},[1706,2241,2242],{},"25",[600,2244,1701],{},[1703,2246,2247,2249],{},[1706,2248,1984],{},[1706,2250,2229],{},[604,2252,2253],{"encoding":606},"3^2 + 4^2 = 25 = 5^2",[568,2255,2257,2304,2348,2366],{"className":2256,"ariaHidden":589},[611],[568,2258,2260,2264,2295,2298,2301],{"className":2259},[615],[568,2261],{"className":2262,"style":2263},[619],"height:0.8974em;vertical-align:-0.0833em;",[568,2265,2267,2270],{"className":2266},[624],[568,2268,2160],{"className":2269},[624],[568,2271,2273],{"className":2272},[1845],[568,2274,2276],{"className":2275},[629],[568,2277,2279],{"className":2278},[633],[568,2280,2283],{"className":2281,"style":2282},[637],"height:0.8141em;",[568,2284,2286,2289],{"style":2285},"top:-3.063em;margin-right:0.05em;",[568,2287],{"className":2288,"style":1861},[644],[568,2290,2292],{"className":2291},[1865,1866,1867,1868],[568,2293,2229],{"className":2294},[624,1868],[568,2296],{"className":2297,"style":1604},[1603],[568,2299,1581],{"className":2300},[1608],[568,2302],{"className":2303,"style":1604},[1603],[568,2305,2307,2310,2339,2342,2345],{"className":2306},[615],[568,2308],{"className":2309,"style":2282},[619],[568,2311,2313,2316],{"className":2312},[624],[568,2314,2165],{"className":2315},[624],[568,2317,2319],{"className":2318},[1845],[568,2320,2322],{"className":2321},[629],[568,2323,2325],{"className":2324},[633],[568,2326,2328],{"className":2327,"style":2282},[637],[568,2329,2330,2333],{"style":2285},[568,2331],{"className":2332,"style":1861},[644],[568,2334,2336],{"className":2335},[1865,1866,1867,1868],[568,2337,2229],{"className":2338},[624,1868],[568,2340],{"className":2341,"style":1816},[1603],[568,2343,1701],{"className":2344},[1820],[568,2346],{"className":2347,"style":1816},[1603],[568,2349,2351,2354,2357,2360,2363],{"className":2350},[615],[568,2352],{"className":2353,"style":1996},[619],[568,2355,2242],{"className":2356},[624],[568,2358],{"className":2359,"style":1816},[1603],[568,2361,1701],{"className":2362},[1820],[568,2364],{"className":2365,"style":1816},[1603],[568,2367,2369,2372],{"className":2368},[615],[568,2370],{"className":2371,"style":2282},[619],[568,2373,2375,2378],{"className":2374},[624],[568,2376,1984],{"className":2377},[624],[568,2379,2381],{"className":2380},[1845],[568,2382,2384],{"className":2383},[629],[568,2385,2387],{"className":2386},[633],[568,2388,2390],{"className":2389,"style":2282},[637],[568,2391,2392,2395],{"style":2285},[568,2393],{"className":2394,"style":1861},[644],[568,2396,2398],{"className":2397},[1865,1866,1867,1868],[568,2399,2229],{"className":2400},[624,1868],". Die Seiten des Dreiecks sind ",[568,2403,2405,2456],{"className":2404},[571],[568,2406,2408],{"className":2407},[575],[577,2409,2410],{"xmlns":579},[581,2411,2412,2453],{},[584,2413,2414,2424,2426,2446,2448],{},[587,2415,2416,2422],{"accent":589},[584,2417,2418,2420],{},[593,2419,595],{},[593,2421,683],{},[600,2423,602],{"stretchy":589},[600,2425,1701],{},[2427,2428,2429],"msqrt",{},[584,2430,2431,2438,2440],{},[1703,2432,2433,2436],{},[1706,2434,2435],{},"8",[1706,2437,2229],{},[600,2439,1581],{},[1703,2441,2442,2444],{},[1706,2443,2165],{},[1706,2445,2229],{},[600,2447,1701],{},[2427,2449,2450],{},[1706,2451,2452],{},"80",[604,2454,2455],{"encoding":606},"\\overline{AC} = \\sqrt{8^2 + 4^2} = \\sqrt{80}",[568,2457,2459,2508,2656],{"className":2458,"ariaHidden":589},[611],[568,2460,2462,2465,2499,2502,2505],{"className":2461},[615],[568,2463],{"className":2464,"style":620},[619],[568,2466,2468],{"className":2467},[624,625],[568,2469,2471],{"className":2470},[629],[568,2472,2474],{"className":2473},[633],[568,2475,2477,2491],{"className":2476,"style":620},[637],[568,2478,2479,2482],{"style":640},[568,2480],{"className":2481,"style":645},[644],[568,2483,2485,2488],{"className":2484},[624],[568,2486,595],{"className":2487},[624,652],[568,2489,683],{"className":2490,"style":699},[624,652],[568,2492,2493,2496],{"style":659},[568,2494],{"className":2495,"style":645},[644],[568,2497],{"className":2498,"style":667},[666],[568,2500],{"className":2501,"style":1816},[1603],[568,2503,1701],{"className":2504},[1820],[568,2506],{"className":2507,"style":1816},[1603],[568,2509,2511,2515,2647,2650,2653],{"className":2510},[615],[568,2512],{"className":2513,"style":2514},[619],"height:1.04em;vertical-align:-0.1266em;",[568,2516,2519],{"className":2517},[624,2518],"sqrt",[568,2520,2523,2638],{"className":2521},[629,2522],"vlist-t2",[568,2524,2526,2633],{"className":2525},[633],[568,2527,2530,2610],{"className":2528,"style":2529},[637],"height:0.9134em;",[568,2531,2534,2537],{"className":2532,"style":640},[2533],"svg-align",[568,2535],{"className":2536,"style":645},[644],[568,2538,2541,2572,2575,2578,2581],{"className":2539,"style":2540},[624],"padding-left:0.833em;",[568,2542,2544,2547],{"className":2543},[624],[568,2545,2435],{"className":2546},[624],[568,2548,2550],{"className":2549},[1845],[568,2551,2553],{"className":2552},[629],[568,2554,2556],{"className":2555},[633],[568,2557,2560],{"className":2558,"style":2559},[637],"height:0.7401em;",[568,2561,2563,2566],{"style":2562},"top:-2.989em;margin-right:0.05em;",[568,2564],{"className":2565,"style":1861},[644],[568,2567,2569],{"className":2568},[1865,1866,1867,1868],[568,2570,2229],{"className":2571},[624,1868],[568,2573],{"className":2574,"style":1604},[1603],[568,2576,1581],{"className":2577},[1608],[568,2579],{"className":2580,"style":1604},[1603],[568,2582,2584,2587],{"className":2583},[624],[568,2585,2165],{"className":2586},[624],[568,2588,2590],{"className":2589},[1845],[568,2591,2593],{"className":2592},[629],[568,2594,2596],{"className":2595},[633],[568,2597,2599],{"className":2598,"style":2559},[637],[568,2600,2601,2604],{"style":2562},[568,2602],{"className":2603,"style":1861},[644],[568,2605,2607],{"className":2606},[1865,1866,1867,1868],[568,2608,2229],{"className":2609},[624,1868],[568,2611,2613,2616],{"style":2612},"top:-2.8734em;",[568,2614],{"className":2615,"style":645},[644],[568,2617,2621],{"className":2618,"style":2620},[2619],"hide-tail","min-width:0.853em;height:1.08em;",[2622,2623,2629],"svg",{"xmlns":2624,"width":2625,"height":2626,"viewBox":2627,"preserveAspectRatio":2628},"http:\u002F\u002Fwww.w3.org\u002F2000\u002Fsvg","400em","1.08em","0 0 400000 1080","xMinYMin slice",[2630,2631],"path",{"d":2632},"M95,702\nc-2.7,0,-7.17,-2.7,-13.5,-8c-5.8,-5.3,-9.5,-10,-9.5,-14\nc0,-2,0.3,-3.3,1,-4c1.3,-2.7,23.83,-20.7,67.5,-54\nc44.2,-33.3,65.8,-50.3,66.5,-51c1.3,-1.3,3,-2,5,-2c4.7,0,8.7,3.3,12,10\ns173,378,173,378c0.7,0,35.3,-71,104,-213c68.7,-142,137.5,-285,206.5,-429\nc69,-144,104.5,-217.7,106.5,-221\nl0 -0\nc5.3,-9.3,12,-14,20,-14\nH400000v40H845.2724\ns-225.272,467,-225.272,467s-235,486,-235,486c-2.7,4.7,-9,7,-19,7\nc-6,0,-10,-1,-12,-3s-194,-422,-194,-422s-65,47,-65,47z\nM834 80h400000v40h-400000z",[568,2634,2637],{"className":2635},[2636],"vlist-s","​",[568,2639,2641],{"className":2640},[633],[568,2642,2645],{"className":2643,"style":2644},[637],"height:0.1266em;",[568,2646],{},[568,2648],{"className":2649,"style":1816},[1603],[568,2651,1701],{"className":2652},[1820],[568,2654],{"className":2655,"style":1816},[1603],[568,2657,2659,2663],{"className":2658},[615],[568,2660],{"className":2661,"style":2662},[619],"height:1.04em;vertical-align:-0.1328em;",[568,2664,2666],{"className":2665},[624,2518],[568,2667,2669,2704],{"className":2668},[629,2522],[568,2670,2672,2701],{"className":2671},[633],[568,2673,2676,2688],{"className":2674,"style":2675},[637],"height:0.9072em;",[568,2677,2679,2682],{"className":2678,"style":640},[2533],[568,2680],{"className":2681,"style":645},[644],[568,2683,2685],{"className":2684,"style":2540},[624],[568,2686,2452],{"className":2687},[624],[568,2689,2691,2694],{"style":2690},"top:-2.8672em;",[568,2692],{"className":2693,"style":645},[644],[568,2695,2697],{"className":2696,"style":2620},[2619],[2622,2698,2699],{"xmlns":2624,"width":2625,"height":2626,"viewBox":2627,"preserveAspectRatio":2628},[2630,2700],{"d":2632},[568,2702,2637],{"className":2703},[2636],[568,2705,2707],{"className":2706},[633],[568,2708,2711],{"className":2709,"style":2710},[637],"height:0.1328em;",[568,2712],{},[568,2714,2716,2765],{"className":2715},[571],[568,2717,2719],{"className":2718},[575],[577,2720,2721],{"xmlns":579},[581,2722,2723,2762],{},[584,2724,2725,2735,2737,2755,2757],{},[587,2726,2727,2733],{"accent":589},[584,2728,2729,2731],{},[593,2730,598],{},[593,2732,683],{},[600,2734,602],{"stretchy":589},[600,2736,1701],{},[2427,2738,2739],{},[584,2740,2741,2747,2749],{},[1703,2742,2743,2745],{},[1706,2744,2229],{},[1706,2746,2229],{},[600,2748,1581],{},[1703,2750,2751,2753],{},[1706,2752,2165],{},[1706,2754,2229],{},[600,2756,1701],{},[2427,2758,2759],{},[1706,2760,2761],{},"20",[604,2763,2764],{"encoding":606},"\\overline{BC} = \\sqrt{2^2 + 4^2} = \\sqrt{20}",[568,2766,2768,2817,2943],{"className":2767,"ariaHidden":589},[611],[568,2769,2771,2774,2808,2811,2814],{"className":2770},[615],[568,2772],{"className":2773,"style":620},[619],[568,2775,2777],{"className":2776},[624,625],[568,2778,2780],{"className":2779},[629],[568,2781,2783],{"className":2782},[633],[568,2784,2786,2800],{"className":2785,"style":620},[637],[568,2787,2788,2791],{"style":640},[568,2789],{"className":2790,"style":645},[644],[568,2792,2794,2797],{"className":2793},[624],[568,2795,598],{"className":2796,"style":656},[624,652],[568,2798,683],{"className":2799,"style":699},[624,652],[568,2801,2802,2805],{"style":659},[568,2803],{"className":2804,"style":645},[644],[568,2806],{"className":2807,"style":667},[666],[568,2809],{"className":2810,"style":1816},[1603],[568,2812,1701],{"className":2813},[1820],[568,2815],{"className":2816,"style":1816},[1603],[568,2818,2820,2823,2934,2937,2940],{"className":2819},[615],[568,2821],{"className":2822,"style":2514},[619],[568,2824,2826],{"className":2825},[624,2518],[568,2827,2829,2926],{"className":2828},[629,2522],[568,2830,2832,2923],{"className":2831},[633],[568,2833,2835,2911],{"className":2834,"style":2529},[637],[568,2836,2838,2841],{"className":2837,"style":640},[2533],[568,2839],{"className":2840,"style":645},[644],[568,2842,2844,2873,2876,2879,2882],{"className":2843,"style":2540},[624],[568,2845,2847,2850],{"className":2846},[624],[568,2848,2229],{"className":2849},[624],[568,2851,2853],{"className":2852},[1845],[568,2854,2856],{"className":2855},[629],[568,2857,2859],{"className":2858},[633],[568,2860,2862],{"className":2861,"style":2559},[637],[568,2863,2864,2867],{"style":2562},[568,2865],{"className":2866,"style":1861},[644],[568,2868,2870],{"className":2869},[1865,1866,1867,1868],[568,2871,2229],{"className":2872},[624,1868],[568,2874],{"className":2875,"style":1604},[1603],[568,2877,1581],{"className":2878},[1608],[568,2880],{"className":2881,"style":1604},[1603],[568,2883,2885,2888],{"className":2884},[624],[568,2886,2165],{"className":2887},[624],[568,2889,2891],{"className":2890},[1845],[568,2892,2894],{"className":2893},[629],[568,2895,2897],{"className":2896},[633],[568,2898,2900],{"className":2899,"style":2559},[637],[568,2901,2902,2905],{"style":2562},[568,2903],{"className":2904,"style":1861},[644],[568,2906,2908],{"className":2907},[1865,1866,1867,1868],[568,2909,2229],{"className":2910},[624,1868],[568,2912,2913,2916],{"style":2612},[568,2914],{"className":2915,"style":645},[644],[568,2917,2919],{"className":2918,"style":2620},[2619],[2622,2920,2921],{"xmlns":2624,"width":2625,"height":2626,"viewBox":2627,"preserveAspectRatio":2628},[2630,2922],{"d":2632},[568,2924,2637],{"className":2925},[2636],[568,2927,2929],{"className":2928},[633],[568,2930,2932],{"className":2931,"style":2644},[637],[568,2933],{},[568,2935],{"className":2936,"style":1816},[1603],[568,2938,1701],{"className":2939},[1820],[568,2941],{"className":2942,"style":1816},[1603],[568,2944,2946,2949],{"className":2945},[615],[568,2947],{"className":2948,"style":2662},[619],[568,2950,2952],{"className":2951},[624,2518],[568,2953,2955,2988],{"className":2954},[629,2522],[568,2956,2958,2985],{"className":2957},[633],[568,2959,2961,2973],{"className":2960,"style":2675},[637],[568,2962,2964,2967],{"className":2963,"style":640},[2533],[568,2965],{"className":2966,"style":645},[644],[568,2968,2970],{"className":2969,"style":2540},[624],[568,2971,2761],{"className":2972},[624],[568,2974,2975,2978],{"style":2690},[568,2976],{"className":2977,"style":645},[644],[568,2979,2981],{"className":2980,"style":2620},[2619],[2622,2982,2983],{"xmlns":2624,"width":2625,"height":2626,"viewBox":2627,"preserveAspectRatio":2628},[2630,2984],{"d":2632},[568,2986,2637],{"className":2987},[2636],[568,2989,2991],{"className":2990},[633],[568,2992,2994],{"className":2993,"style":2710},[637],[568,2995],{},[568,2997,2999,3026],{"className":2998},[571],[568,3000,3002],{"className":3001},[575],[577,3003,3004],{"xmlns":579},[581,3005,3006,3023],{},[584,3007,3008,3018,3020],{},[587,3009,3010,3016],{"accent":589},[584,3011,3012,3014],{},[593,3013,595],{},[593,3015,598],{},[600,3017,602],{"stretchy":589},[600,3019,1701],{},[1706,3021,3022],{},"10",[604,3024,3025],{"encoding":606},"\\overline{AB} = 10",[568,3027,3029,3078],{"className":3028,"ariaHidden":589},[611],[568,3030,3032,3035,3069,3072,3075],{"className":3031},[615],[568,3033],{"className":3034,"style":620},[619],[568,3036,3038],{"className":3037},[624,625],[568,3039,3041],{"className":3040},[629],[568,3042,3044],{"className":3043},[633],[568,3045,3047,3061],{"className":3046,"style":620},[637],[568,3048,3049,3052],{"style":640},[568,3050],{"className":3051,"style":645},[644],[568,3053,3055,3058],{"className":3054},[624],[568,3056,595],{"className":3057},[624,652],[568,3059,598],{"className":3060,"style":656},[624,652],[568,3062,3063,3066],{"style":659},[568,3064],{"className":3065,"style":645},[644],[568,3067],{"className":3068,"style":667},[666],[568,3070],{"className":3071,"style":1816},[1603],[568,3073,1701],{"className":3074},[1820],[568,3076],{"className":3077,"style":1816},[1603],[568,3079,3081,3084],{"className":3080},[615],[568,3082],{"className":3083,"style":1996},[619],[568,3085,3022],{"className":3086},[624],". Pythagoras bestätigt den rechten Winkel bei ",[568,3089,3091,3104],{"className":3090},[571],[568,3092,3094],{"className":3093},[575],[577,3095,3096],{"xmlns":579},[581,3097,3098,3102],{},[584,3099,3100],{},[593,3101,683],{},[604,3103,683],{"encoding":606},[568,3105,3107],{"className":3106,"ariaHidden":589},[611],[568,3108,3110,3113],{"className":3109},[615],[568,3111],{"className":3112,"style":695},[619],[568,3114,683],{"className":3115,"style":699},[624,652],[568,3117,3119],{"className":3118},[1664],[568,3120,3122,3153],{"className":3121},[571],[568,3123,3125],{"className":3124},[575],[577,3126,3127],{"xmlns":579,"display":1673},[581,3128,3129,3150],{},[584,3130,3131,3133,3135,3137,3139,3142,3144],{},[1706,3132,2452],{},[600,3134,1581],{},[1706,3136,2761],{},[600,3138,1701],{},[1706,3140,3141],{},"100",[600,3143,1701],{},[1703,3145,3146,3148],{},[1706,3147,3022],{},[1706,3149,2229],{},[604,3151,3152],{"encoding":606},"80 + 20 = 100 = 10^2",[568,3154,3156,3175,3193,3211],{"className":3155,"ariaHidden":589},[611],[568,3157,3159,3163,3166,3169,3172],{"className":3158},[615],[568,3160],{"className":3161,"style":3162},[619],"height:0.7278em;vertical-align:-0.0833em;",[568,3164,2452],{"className":3165},[624],[568,3167],{"className":3168,"style":1604},[1603],[568,3170,1581],{"className":3171},[1608],[568,3173],{"className":3174,"style":1604},[1603],[568,3176,3178,3181,3184,3187,3190],{"className":3177},[615],[568,3179],{"className":3180,"style":1996},[619],[568,3182,2761],{"className":3183},[624],[568,3185],{"className":3186,"style":1816},[1603],[568,3188,1701],{"className":3189},[1820],[568,3191],{"className":3192,"style":1816},[1603],[568,3194,3196,3199,3202,3205,3208],{"className":3195},[615],[568,3197],{"className":3198,"style":1996},[619],[568,3200,3141],{"className":3201},[624],[568,3203],{"className":3204,"style":1816},[1603],[568,3206,1701],{"className":3207},[1820],[568,3209],{"className":3210,"style":1816},[1603],[568,3212,3214,3218,3222],{"className":3213},[615],[568,3215],{"className":3216,"style":3217},[619],"height:0.8641em;",[568,3219,3221],{"className":3220},[624],"1",[568,3223,3225,3228],{"className":3224},[624],[568,3226,1841],{"className":3227},[624],[568,3229,3231],{"className":3230},[1845],[568,3232,3234],{"className":3233},[629],[568,3235,3237],{"className":3236},[633],[568,3238,3240],{"className":3239,"style":3217},[637],[568,3241,3242,3245],{"style":1857},[568,3243],{"className":3244,"style":1861},[644],[568,3246,3248],{"className":3247},[1865,1866,1867,1868],[568,3249,2229],{"className":3250},[624,1868],[564,3252,3253,3254,1196,3302,3344,3345,3387],{},"Ein rechtwinkliges Dreieck hat die Katheten ",[568,3255,3257,3279],{"className":3256},[571],[568,3258,3260],{"className":3259},[575],[577,3261,3262],{"xmlns":579},[581,3263,3264,3276],{},[584,3265,3266,3269,3273],{},[1706,3267,3268],{},"6",[3270,3271,3272],"mtext",{}," ",[3270,3274,3275],{},"cm",[604,3277,3278],{"encoding":606},"6\\,\\text{cm}",[568,3280,3282],{"className":3281,"ariaHidden":589},[611],[568,3283,3285,3288,3291,3295],{"className":3284},[615],[568,3286],{"className":3287,"style":1996},[619],[568,3289,3268],{"className":3290},[624],[568,3292],{"className":3293,"style":3294},[1603],"margin-right:0.1667em;",[568,3296,3299],{"className":3297},[624,3298],"text",[568,3300,3275],{"className":3301},[624],[568,3303,3305,3323],{"className":3304},[571],[568,3306,3308],{"className":3307},[575],[577,3309,3310],{"xmlns":579},[581,3311,3312,3320],{},[584,3313,3314,3316,3318],{},[1706,3315,2435],{},[3270,3317,3272],{},[3270,3319,3275],{},[604,3321,3322],{"encoding":606},"8\\,\\text{cm}",[568,3324,3326],{"className":3325,"ariaHidden":589},[611],[568,3327,3329,3332,3335,3338],{"className":3328},[615],[568,3330],{"className":3331,"style":1996},[619],[568,3333,2435],{"className":3334},[624],[568,3336],{"className":3337,"style":3294},[1603],[568,3339,3341],{"className":3340},[624,3298],[568,3342,3275],{"className":3343},[624],", also die Hypotenuse ",[568,3346,3348,3366],{"className":3347},[571],[568,3349,3351],{"className":3350},[575],[577,3352,3353],{"xmlns":579},[581,3354,3355,3363],{},[584,3356,3357,3359,3361],{},[1706,3358,3022],{},[3270,3360,3272],{},[3270,3362,3275],{},[604,3364,3365],{"encoding":606},"10\\,\\text{cm}",[568,3367,3369],{"className":3368,"ariaHidden":589},[611],[568,3370,3372,3375,3378,3381],{"className":3371},[615],[568,3373],{"className":3374,"style":1996},[619],[568,3376,3022],{"className":3377},[624],[568,3379],{"className":3380,"style":3294},[1603],[568,3382,3384],{"className":3383},[624,3298],[568,3385,3275],{"className":3386},[624],". Sein Umkreis hat den Radius:",[568,3389,3391],{"className":3390},[1664],[568,3392,3394,3432],{"className":3393},[571],[568,3395,3397],{"className":3396},[575],[577,3398,3399],{"xmlns":579,"display":1673},[581,3400,3401,3429],{},[584,3402,3403,3406,3408,3421,3423,3425,3427],{},[593,3404,3405],{},"r",[600,3407,1701],{},[3409,3410,3411,3419],"mfrac",{},[584,3412,3413,3415,3417],{},[1706,3414,3022],{},[3270,3416,3272],{},[3270,3418,3275],{},[1706,3420,2229],{},[600,3422,1701],{},[1706,3424,1984],{},[3270,3426,3272],{},[3270,3428,3275],{},[604,3430,3431],{"encoding":606},"r = \\frac{10\\,\\text{cm}}{2} = 5\\,\\text{cm}",[568,3433,3435,3454,3548],{"className":3434,"ariaHidden":589},[611],[568,3436,3438,3441,3445,3448,3451],{"className":3437},[615],[568,3439],{"className":3440,"style":1411},[619],[568,3442,3405],{"className":3443,"style":3444},[624,652],"margin-right:0.0278em;",[568,3446],{"className":3447,"style":1816},[1603],[568,3449,1701],{"className":3450},[1820],[568,3452],{"className":3453,"style":1816},[1603],[568,3455,3457,3461,3539,3542,3545],{"className":3456},[615],[568,3458],{"className":3459,"style":3460},[619],"height:2.0074em;vertical-align:-0.686em;",[568,3462,3464,3468,3536],{"className":3463},[624],[568,3465],{"className":3466},[1787,3467],"nulldelimiter",[568,3469,3471],{"className":3470},[3409],[568,3472,3474,3527],{"className":3473},[629,2522],[568,3475,3477,3524],{"className":3476},[633],[568,3478,3481,3493,3503],{"className":3479,"style":3480},[637],"height:1.3214em;",[568,3482,3484,3487],{"style":3483},"top:-2.314em;",[568,3485],{"className":3486,"style":645},[644],[568,3488,3490],{"className":3489},[624],[568,3491,2229],{"className":3492},[624],[568,3494,3496,3499],{"style":3495},"top:-3.23em;",[568,3497],{"className":3498,"style":645},[644],[568,3500],{"className":3501,"style":667},[3502],"frac-line",[568,3504,3506,3509],{"style":3505},"top:-3.677em;",[568,3507],{"className":3508,"style":645},[644],[568,3510,3512,3515,3518],{"className":3511},[624],[568,3513,3022],{"className":3514},[624],[568,3516],{"className":3517,"style":3294},[1603],[568,3519,3521],{"className":3520},[624,3298],[568,3522,3275],{"className":3523},[624],[568,3525,2637],{"className":3526},[2636],[568,3528,3530],{"className":3529},[633],[568,3531,3534],{"className":3532,"style":3533},[637],"height:0.686em;",[568,3535],{},[568,3537],{"className":3538},[1812,3467],[568,3540],{"className":3541,"style":1816},[1603],[568,3543,1701],{"className":3544},[1820],[568,3546],{"className":3547,"style":1816},[1603],[568,3549,3551,3554,3557,3560],{"className":3550},[615],[568,3552],{"className":3553,"style":1996},[619],[568,3555,1984],{"className":3556},[624],[568,3558],{"className":3559,"style":3294},[1603],[568,3561,3563],{"className":3562},[624,3298],[568,3564,3275],{"className":3565},[624],[559,3567,3569],{"id":3568},"typische-fehler","Typische Fehler",[941,3571,3572,3662,3757],{},[944,3573,3574,3575,3603,3604,3632,3633,3661],{},"Den rechten Winkel bei ",[568,3576,3578,3591],{"className":3577},[571],[568,3579,3581],{"className":3580},[575],[577,3582,3583],{"xmlns":579},[581,3584,3585,3589],{},[584,3586,3587],{},[593,3588,595],{},[604,3590,595],{"encoding":606},[568,3592,3594],{"className":3593,"ariaHidden":589},[611],[568,3595,3597,3600],{"className":3596},[615],[568,3598],{"className":3599,"style":695},[619],[568,3601,595],{"className":3602},[624,652]," oder ",[568,3605,3607,3620],{"className":3606},[571],[568,3608,3610],{"className":3609},[575],[577,3611,3612],{"xmlns":579},[581,3613,3614,3618],{},[584,3615,3616],{},[593,3617,598],{},[604,3619,598],{"encoding":606},[568,3621,3623],{"className":3622,"ariaHidden":589},[611],[568,3624,3626,3629],{"className":3625},[615],[568,3627],{"className":3628,"style":695},[619],[568,3630,598],{"className":3631,"style":656},[624,652]," suchen. Der rechte Winkel liegt immer bei dem Punkt ",[568,3634,3636,3649],{"className":3635},[571],[568,3637,3639],{"className":3638},[575],[577,3640,3641],{"xmlns":579},[581,3642,3643,3647],{},[584,3644,3645],{},[593,3646,683],{},[604,3648,683],{"encoding":606},[568,3650,3652],{"className":3651,"ariaHidden":589},[611],[568,3653,3655,3658],{"className":3654},[615],[568,3656],{"className":3657,"style":695},[619],[568,3659,683],{"className":3660,"style":699},[624,652]," auf dem Kreis, gegenüber dem Durchmesser.",[944,3663,3664,3665,3693,3694,806],{},"Den Satz für eine Sehne anwenden, die kein Durchmesser ist. Dann ist der Winkel bei ",[568,3666,3668,3681],{"className":3667},[571],[568,3669,3671],{"className":3670},[575],[577,3672,3673],{"xmlns":579},[581,3674,3675,3679],{},[584,3676,3677],{},[593,3678,683],{},[604,3680,683],{"encoding":606},[568,3682,3684],{"className":3683,"ariaHidden":589},[611],[568,3685,3687,3690],{"className":3686},[615],[568,3688],{"className":3689,"style":695},[619],[568,3691,683],{"className":3692,"style":699},[624,652]," nicht ",[568,3695,3697,3715],{"className":3696},[571],[568,3698,3700],{"className":3699},[575],[577,3701,3702],{"xmlns":579},[581,3703,3704,3712],{},[584,3705,3706],{},[1703,3707,3708,3710],{},[1706,3709,1732],{},[600,3711,1711],{},[604,3713,3714],{"encoding":606},"90^\\circ",[568,3716,3718],{"className":3717,"ariaHidden":589},[611],[568,3719,3721,3725,3728],{"className":3720},[615],[568,3722],{"className":3723,"style":3724},[619],"height:0.6741em;",[568,3726,1933],{"className":3727},[624],[568,3729,3731,3734],{"className":3730},[624],[568,3732,1841],{"className":3733},[624],[568,3735,3737],{"className":3736},[1845],[568,3738,3740],{"className":3739},[629],[568,3741,3743],{"className":3742},[633],[568,3744,3746],{"className":3745,"style":3724},[637],[568,3747,3748,3751],{"style":2285},[568,3749],{"className":3750,"style":1861},[644],[568,3752,3754],{"className":3753},[1865,1866,1867,1868],[568,3755,1711],{"className":3756},[1608,1868],[944,3758,3759],{},"Beim Umkreis den Durchmesser mit dem Radius verwechseln: Die Hypotenuse ist der Durchmesser, der Radius ist ihre Hälfte.",{"title":3761,"searchDepth":3762,"depth":3762,"links":3763},"",2,[3764,3765,3766,3767],{"id":561,"depth":3762,"text":562},{"id":955,"depth":3762,"text":956},{"id":1965,"depth":3762,"text":1966},{"id":3568,"depth":3762,"text":3569},[3769,3771,3774,3776,3779],{"lhs":3770,"rhs":1841},"(-r - r*cos(t))*(r - r*cos(t)) + (0 - r*sin(t))*(0 - r*sin(t))",{"lhs":3772,"rhs":3773},"3^2 + 4^2","5^2",{"lhs":3775,"rhs":1841},"(-5 - 3)*(5 - 3) + (0 - 4)*(0 - 4)",{"lhs":3777,"rhs":3778},"sqrt(8^2 + 4^2)^2 + sqrt(2^2 + 4^2)^2","10^2",{"lhs":3780,"rhs":1984},"sqrt(6^2 + 8^2)\u002F2","C\\ \\text{liegt auf dem Kreis mit dem Durchmesser}\\ \\overline{AB},\\ C \\neq A,\\ C \\neq B","\u003Cspan class=\"katex\">\u003Cspan class=\"katex-mathml\">\u003Cmath xmlns=\"http:\u002F\u002Fwww.w3.org\u002F1998\u002FMath\u002FMathML\">\u003Csemantics>\u003Cmrow>\u003Cmi>C\u003C\u002Fmi>\u003C\u002Fmrow>\u003Cannotation encoding=\"application\u002Fx-tex\">C\u003C\u002Fannotation>\u003C\u002Fsemantics>\u003C\u002Fmath>\u003C\u002Fspan>\u003Cspan class=\"katex-html\" aria-hidden=\"true\">\u003Cspan class=\"katex-base\">\u003Cspan class=\"katex-strut\" style=\"height:0.6833em;\">\u003C\u002Fspan>\u003Cspan class=\"mord mathnormal\" style=\"margin-right:0.0715em;\">C\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan> \u003Cspan class=\"katex\">liegt auf dem Kreis mit dem Durchmesser\u003C\u002Fspan> \u003Cspan class=\"katex\">\u003Cspan class=\"katex-mathml\">\u003Cmath xmlns=\"http:\u002F\u002Fwww.w3.org\u002F1998\u002FMath\u002FMathML\">\u003Csemantics>\u003Cmrow>\u003Cmover accent=\"true\">\u003Cmrow>\u003Cmi>A\u003C\u002Fmi>\u003Cmi>B\u003C\u002Fmi>\u003C\u002Fmrow>\u003Cmo stretchy=\"true\">‾\u003C\u002Fmo>\u003C\u002Fmover>\u003Cmo separator=\"true\">,\u003C\u002Fmo>\u003C\u002Fmrow>\u003Cannotation encoding=\"application\u002Fx-tex\">\\overline{AB},\u003C\u002Fannotation>\u003C\u002Fsemantics>\u003C\u002Fmath>\u003C\u002Fspan>\u003Cspan class=\"katex-html\" aria-hidden=\"true\">\u003Cspan class=\"katex-base\">\u003Cspan class=\"katex-strut\" style=\"height:1.0778em;vertical-align:-0.1944em;\">\u003C\u002Fspan>\u003Cspan class=\"mord katex-overline\">\u003Cspan class=\"vlist-t\">\u003Cspan class=\"vlist-r\">\u003Cspan class=\"vlist\" style=\"height:0.8833em;\">\u003Cspan style=\"top:-3em;\">\u003Cspan class=\"pstrut\" style=\"height:3em;\">\u003C\u002Fspan>\u003Cspan class=\"mord\">\u003Cspan class=\"mord mathnormal\">A\u003C\u002Fspan>\u003Cspan class=\"mord mathnormal\" style=\"margin-right:0.0502em;\">B\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan style=\"top:-3.8033em;\">\u003Cspan class=\"pstrut\" style=\"height:3em;\">\u003C\u002Fspan>\u003Cspan class=\"overline-line\" style=\"border-bottom-width:0.04em;\">\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"mpunct\">,\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan> \u003Cspan class=\"katex\">\u003Cspan class=\"katex-mathml\">\u003Cmath xmlns=\"http:\u002F\u002Fwww.w3.org\u002F1998\u002FMath\u002FMathML\">\u003Csemantics>\u003Cmrow>\u003Cmi>C\u003C\u002Fmi>\u003Cmo mathvariant=\"normal\">≠\u003C\u002Fmo>\u003Cmi>A\u003C\u002Fmi>\u003Cmo separator=\"true\">,\u003C\u002Fmo>\u003C\u002Fmrow>\u003Cannotation encoding=\"application\u002Fx-tex\">C \\neq A,\u003C\u002Fannotation>\u003C\u002Fsemantics>\u003C\u002Fmath>\u003C\u002Fspan>\u003Cspan class=\"katex-html\" aria-hidden=\"true\">\u003Cspan class=\"katex-base\">\u003Cspan class=\"katex-strut\" style=\"height:0.8889em;vertical-align:-0.1944em;\">\u003C\u002Fspan>\u003Cspan class=\"mord mathnormal\" style=\"margin-right:0.0715em;\">C\u003C\u002Fspan>\u003Cspan class=\"mspace\" style=\"margin-right:0.2778em;\">\u003C\u002Fspan>\u003Cspan class=\"mrel\">\u003Cspan class=\"mrel\">\u003Cspan class=\"mord katex-vbox\">\u003Cspan class=\"katex-thinbox\">\u003Cspan class=\"rlap\">\u003Cspan class=\"katex-strut\" style=\"height:0.8889em;vertical-align:-0.1944em;\">\u003C\u002Fspan>\u003Cspan class=\"katex-inner\">\u003Cspan class=\"mord\">\u003Cspan class=\"mrel\">\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"katex-fix\">\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"mspace nobreak\">\u003C\u002Fspan>\u003Cspan class=\"mrel\">=\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"mspace\" style=\"margin-right:0.2778em;\">\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"katex-base\">\u003Cspan class=\"katex-strut\" style=\"height:0.8778em;vertical-align:-0.1944em;\">\u003C\u002Fspan>\u003Cspan class=\"mord mathnormal\">A\u003C\u002Fspan>\u003Cspan class=\"mpunct\">,\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan> \u003Cspan class=\"katex\">\u003Cspan class=\"katex-mathml\">\u003Cmath xmlns=\"http:\u002F\u002Fwww.w3.org\u002F1998\u002FMath\u002FMathML\">\u003Csemantics>\u003Cmrow>\u003Cmi>C\u003C\u002Fmi>\u003Cmo mathvariant=\"normal\">≠\u003C\u002Fmo>\u003Cmi>B\u003C\u002Fmi>\u003C\u002Fmrow>\u003Cannotation encoding=\"application\u002Fx-tex\">C \\neq B\u003C\u002Fannotation>\u003C\u002Fsemantics>\u003C\u002Fmath>\u003C\u002Fspan>\u003Cspan class=\"katex-html\" aria-hidden=\"true\">\u003Cspan class=\"katex-base\">\u003Cspan class=\"katex-strut\" style=\"height:0.8889em;vertical-align:-0.1944em;\">\u003C\u002Fspan>\u003Cspan class=\"mord mathnormal\" style=\"margin-right:0.0715em;\">C\u003C\u002Fspan>\u003Cspan class=\"mspace\" style=\"margin-right:0.2778em;\">\u003C\u002Fspan>\u003Cspan class=\"mrel\">\u003Cspan class=\"mrel\">\u003Cspan class=\"mord katex-vbox\">\u003Cspan class=\"katex-thinbox\">\u003Cspan class=\"rlap\">\u003Cspan class=\"katex-strut\" style=\"height:0.8889em;vertical-align:-0.1944em;\">\u003C\u002Fspan>\u003Cspan class=\"katex-inner\">\u003Cspan class=\"mord\">\u003Cspan class=\"mrel\">\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"katex-fix\">\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"mspace nobreak\">\u003C\u002Fspan>\u003Cspan class=\"mrel\">=\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"mspace\" style=\"margin-right:0.2778em;\">\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"katex-base\">\u003Cspan class=\"katex-strut\" style=\"height:0.6833em;\">\u003C\u002Fspan>\u003Cspan class=\"mord mathnormal\" style=\"margin-right:0.0502em;\">B\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>",null,"md",{"caption":3786,"x":3787,"y":3790,"items":3793},"Dreieck über dem Durchmesser AB eines Kreises, die Ecke C liegt auf dem Kreis",[3788,3789],-2.7,2.7,[3791,3792],-2.4,2.5,[3794,3799,3809,3814,3820,3824,3829,3834],{"type":3795,"center":3796,"r":3762,"style":3798},"circle",[3797,3797],0,"muted",{"type":3800,"points":3801,"fill":3808},"polygon",[3802,3804,3805],[3803,3797],-2,[3762,3797],[3806,3807],1,1.7321,true,{"type":3810,"at":3811,"from":3812,"to":3813},"rightAngle",[3806,3807],[3803,3797],[3762,3797],{"type":3815,"at":3816,"label":595,"offset":3817},"point",[3803,3797],[3818,3819],-18,4,{"type":3815,"at":3821,"label":598,"offset":3822},[3762,3797],[3823,3819],8,{"type":3815,"at":3825,"label":683,"offset":3826},[3806,3807],[3827,3828],6,-10,{"type":3815,"at":3830,"label":974,"offset":3831},[3797,3797],[3832,3833],-6,16,{"type":3835,"at":3836,"text":3839},"label",[3837,3838],0.55,1.15,"γ","\u003Csvg xmlns=\"http:\u002F\u002Fwww.w3.org\u002F2000\u002Fsvg\" viewBox=\"0 0 259.2 235.2\" width=\"259.2\" height=\"235.2\" role=\"img\" aria-label=\"Dreieck über dem Durchmesser AB eines Kreises, die Ecke C liegt auf dem Kreis\" class=\"formula-figure-svg\">\u003Cdefs>\u003Cmarker id=\"fig-thales-theorem-arrow\" viewBox=\"0 0 10 10\" refX=\"9\" refY=\"5\" markerWidth=\"7\" markerHeight=\"7\" orient=\"auto-start-reverse\">\u003Cpath d=\"M 0 0 L 10 5 L 0 10 z\" class=\"fig-arrowhead\"\u002F>\u003C\u002Fmarker>\u003CclipPath id=\"fig-thales-theorem-clip\">\u003Crect x=\"0\" y=\"0\" width=\"259.2\" height=\"235.2\"\u002F>\u003C\u002FclipPath>\u003C\u002Fdefs>\u003Ccircle cx=\"129.6\" cy=\"120\" r=\"96\" class=\"fig-muted\"\u002F>\u003Cpolygon points=\"33.6,120 225.6,120 177.6,36.86\" class=\"fig-main fig-fill\"\u002F>\u003Cpath d=\"M 167.21 42.86 L 173.21 53.25 L 183.6 47.25\" class=\"fig-mark\"\u002F>\u003Ccircle cx=\"175.4\" cy=\"45.06\" r=\"1.5\" class=\"fig-dot\"\u002F>\u003Ccircle cx=\"33.6\" cy=\"120\" r=\"3\" class=\"fig-dot\"\u002F>\u003Ctext x=\"15.600000000000001\" y=\"124\" text-anchor=\"start\" dominant-baseline=\"middle\" class=\"fig-label fig-upright\">A\u003C\u002Ftext>\u003Ccircle cx=\"225.6\" cy=\"120\" r=\"3\" class=\"fig-dot\"\u002F>\u003Ctext x=\"233.6\" y=\"124\" text-anchor=\"start\" dominant-baseline=\"middle\" class=\"fig-label fig-upright\">B\u003C\u002Ftext>\u003Ccircle cx=\"177.6\" cy=\"36.86\" r=\"3\" class=\"fig-dot\"\u002F>\u003Ctext x=\"183.6\" y=\"26.86\" text-anchor=\"start\" dominant-baseline=\"middle\" class=\"fig-label fig-upright\">C\u003C\u002Ftext>\u003Ccircle cx=\"129.6\" cy=\"120\" r=\"3\" class=\"fig-dot\"\u002F>\u003Ctext x=\"123.6\" y=\"136\" text-anchor=\"start\" dominant-baseline=\"middle\" class=\"fig-label fig-upright\">M\u003C\u002Ftext>\u003Ctext x=\"156\" y=\"64.8\" text-anchor=\"middle\" dominant-baseline=\"middle\" class=\"fig-label\">γ\u003C\u002Ftext>\u003C\u002Fsvg>","thales-theorem","\\gamma = 90^\\circ","\u003Cspan class=\"katex-display\">\u003Cspan class=\"katex\">\u003Cspan class=\"katex-mathml\">\u003Cmath xmlns=\"http:\u002F\u002Fwww.w3.org\u002F1998\u002FMath\u002FMathML\" display=\"block\">\u003Csemantics>\u003Cmrow>\u003Cmi>γ\u003C\u002Fmi>\u003Cmo>=\u003C\u002Fmo>\u003Cmsup>\u003Cmn>90\u003C\u002Fmn>\u003Cmo>∘\u003C\u002Fmo>\u003C\u002Fmsup>\u003C\u002Fmrow>\u003Cannotation encoding=\"application\u002Fx-tex\">\\gamma = 90^\\circ\u003C\u002Fannotation>\u003C\u002Fsemantics>\u003C\u002Fmath>\u003C\u002Fspan>\u003Cspan class=\"katex-html\" aria-hidden=\"true\">\u003Cspan class=\"katex-base\">\u003Cspan class=\"katex-strut\" style=\"height:0.625em;vertical-align:-0.1944em;\">\u003C\u002Fspan>\u003Cspan class=\"mord mathnormal\" style=\"margin-right:0.0556em;\">γ\u003C\u002Fspan>\u003Cspan class=\"mspace\" style=\"margin-right:0.2778em;\">\u003C\u002Fspan>\u003Cspan class=\"mrel\">=\u003C\u002Fspan>\u003Cspan class=\"mspace\" style=\"margin-right:0.2778em;\">\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"katex-base\">\u003Cspan class=\"katex-strut\" style=\"height:0.7241em;\">\u003C\u002Fspan>\u003Cspan class=\"mord\">9\u003C\u002Fspan>\u003Cspan class=\"mord\">\u003Cspan class=\"mord\">0\u003C\u002Fspan>\u003Cspan class=\"msupsub\">\u003Cspan class=\"vlist-t\">\u003Cspan class=\"vlist-r\">\u003Cspan class=\"vlist\" style=\"height:0.7241em;\">\u003Cspan style=\"top:-3.113em;margin-right:0.05em;\">\u003Cspan class=\"pstrut\" style=\"height:2.7em;\">\u003C\u002Fspan>\u003Cspan class=\"katex-sizing reset-size6 size3 mtight\">\u003Cspan class=\"mbin mtight\">∘\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>","middle",{},"\u002Fde\u002Fformulas\u002Fmath\u002Fgeometry\u002Fsatz-des-thales",[],[3849,3850,3851],"triangle-angle-sum","pythagorean-theorem","circle-equation",{"title":548,"description":3761},"de\u002Fformulas\u002Fmath\u002Fgeometry\u002Fsatz-des-thales","Liegt C auf einem Kreis mit dem Durchmesser AB, dann hat das Dreieck ABC bei C einen rechten 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class=\"mord mathnormal\" style=\"margin-right:0.0502em;\">B\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>",{"symbol":683,"meaning":3866,"symbolHtml":3867},"beliebiger weiterer Punkt auf dem Kreis","\u003Cspan class=\"katex\">\u003Cspan class=\"katex-mathml\">\u003Cmath xmlns=\"http:\u002F\u002Fwww.w3.org\u002F1998\u002FMath\u002FMathML\">\u003Csemantics>\u003Cmrow>\u003Cmi>C\u003C\u002Fmi>\u003C\u002Fmrow>\u003Cannotation encoding=\"application\u002Fx-tex\">C\u003C\u002Fannotation>\u003C\u002Fsemantics>\u003C\u002Fmath>\u003C\u002Fspan>\u003Cspan class=\"katex-html\" aria-hidden=\"true\">\u003Cspan class=\"katex-base\">\u003Cspan class=\"katex-strut\" style=\"height:0.6833em;\">\u003C\u002Fspan>\u003Cspan class=\"mord mathnormal\" style=\"margin-right:0.0715em;\">C\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>",{"symbol":3869,"meaning":3870,"symbolHtml":3871},"\\gamma","Winkel des Dreiecks ABC bei C","\u003Cspan class=\"katex\">\u003Cspan class=\"katex-mathml\">\u003Cmath xmlns=\"http:\u002F\u002Fwww.w3.org\u002F1998\u002FMath\u002FMathML\">\u003Csemantics>\u003Cmrow>\u003Cmi>γ\u003C\u002Fmi>\u003C\u002Fmrow>\u003Cannotation encoding=\"application\u002Fx-tex\">\\gamma\u003C\u002Fannotation>\u003C\u002Fsemantics>\u003C\u002Fmath>\u003C\u002Fspan>\u003Cspan class=\"katex-html\" aria-hidden=\"true\">\u003Cspan class=\"katex-base\">\u003Cspan class=\"katex-strut\" style=\"height:0.625em;vertical-align:-0.1944em;\">\u003C\u002Fspan>\u003Cspan class=\"mord mathnormal\" style=\"margin-right:0.0556em;\">γ\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>","lzexPxoLDXePuFpJuRXXxcYDIFmd19ePbK6XpChC-rw",[3874,3877,3880],{"stem":3875,"title":3876,"category":247},"de\u002Fformulas\u002Fmath\u002Fgeometry\u002Fkreisgleichung","Kreisgleichung",{"stem":3878,"title":3879,"category":247},"de\u002Fformulas\u002Fmath\u002Fgeometry\u002Fsatz-des-pythagoras","Satz des 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