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Beide Sekantenabschnitte werden von ",[567,948,950,963],{"className":949},[570],[567,951,953],{"className":952},[574],[576,954,955],{"xmlns":578},[580,956,957,961],{},[583,958,959],{},[586,960,588],{},[590,962,588],{"encoding":592},[567,964,966],{"className":965,"ariaHidden":597},[596],[567,967,969,972],{"className":968},[601],[567,970],{"className":971,"style":606},[605],[567,973,588],{"className":974,"style":612},[610,611]," aus gemessen.",[563,977,978,979,1007,1008,1010,1011,1273],{},"Für zwei Sekanten durch ",[567,980,982,995],{"className":981},[570],[567,983,985],{"className":984},[574],[576,986,987],{"xmlns":578},[580,988,989,993],{},[583,990,991],{},[586,992,588],{},[590,994,588],{"encoding":592},[567,996,998],{"className":997,"ariaHidden":597},[596],[567,999,1001,1004],{"className":1000},[601],[567,1002],{"className":1003,"style":606},[605],[567,1005,588],{"className":1006,"style":612},[610,611]," folgt daraus der ",[622,1009,552],{},": ",[567,1012,1014,1076],{"className":1013},[570],[567,1015,1017],{"className":1016},[574],[576,1018,1019],{"xmlns":578},[580,1020,1021,1073],{},[583,1022,1023,1033,1036,1046,1049,1060,1062],{},[739,1024,1025,1031],{"accent":597},[583,1026,1027,1029],{},[586,1028,588],{},[586,1030,676],{},[748,1032,750],{"stretchy":597},[748,1034,1035],{},"⋅",[739,1037,1038,1044],{"accent":597},[583,1039,1040,1042],{},[586,1041,588],{},[586,1043,706],{},[748,1045,750],{"stretchy":597},[748,1047,1048],{},"=",[739,1050,1051,1058],{"accent":597},[583,1052,1053,1055],{},[586,1054,588],{},[586,1056,1057],{},"C",[748,1059,750],{"stretchy":597},[748,1061,1035],{},[739,1063,1064,1071],{"accent":597},[583,1065,1066,1068],{},[586,1067,588],{},[586,1069,1070],{},"D",[748,1072,750],{"stretchy":597},[590,1074,1075],{"encoding":592},"\\overline{PA} \\cdot \\overline{PB} = \\overline{PC} \\cdot \\overline{PD}",[567,1077,1079,1131,1182,1232],{"className":1078,"ariaHidden":597},[596],[567,1080,1082,1085,1119,1124,1128],{"className":1081},[601],[567,1083],{"className":1084,"style":763},[605],[567,1086,1088],{"className":1087},[610,767],[567,1089,1091],{"className":1090},[771],[567,1092,1094],{"className":1093},[775],[567,1095,1097,1111],{"className":1096,"style":763},[779],[567,1098,1099,1102],{"style":782},[567,1100],{"className":1101,"style":787},[786],[567,1103,1105,1108],{"className":1104},[610],[567,1106,588],{"className":1107,"style":612},[610,611],[567,1109,676],{"className":1110},[610,611],[567,1112,1113,1116],{"style":799},[567,1114],{"className":1115,"style":787},[786],[567,1117],{"className":1118,"style":807},[806],[567,1120],{"className":1121,"style":1123},[1122],"mspace","margin-right:0.2222em;",[567,1125,1035],{"className":1126},[1127],"mbin",[567,1129],{"className":1130,"style":1123},[1122],[567,1132,1134,1137,1171,1175,1179],{"className":1133},[601],[567,1135],{"className":1136,"style":763},[605],[567,1138,1140],{"className":1139},[610,767],[567,1141,1143],{"className":1142},[771],[567,1144,1146],{"className":1145},[775],[567,1147,1149,1163],{"className":1148,"style":763},[779],[567,1150,1151,1154],{"style":782},[567,1152],{"className":1153,"style":787},[786],[567,1155,1157,1160],{"className":1156},[610],[567,1158,588],{"className":1159,"style":612},[610,611],[567,1161,706],{"className":1162,"style":721},[610,611],[567,1164,1165,1168],{"style":799},[567,1166],{"className":1167,"style":787},[786],[567,1169],{"className":1170,"style":807},[806],[567,1172],{"className":1173,"style":1174},[1122],"margin-right:0.2778em;",[567,1176,1048],{"className":1177},[1178],"mrel",[567,1180],{"className":1181,"style":1174},[1122],[567,1183,1185,1188,1223,1226,1229],{"className":1184},[601],[567,1186],{"className":1187,"style":763},[605],[567,1189,1191],{"className":1190},[610,767],[567,1192,1194],{"className":1193},[771],[567,1195,1197],{"className":1196},[775],[567,1198,1200,1215],{"className":1199,"style":763},[779],[567,1201,1202,1205],{"style":782},[567,1203],{"className":1204,"style":787},[786],[567,1206,1208,1211],{"className":1207},[610],[567,1209,588],{"className":1210,"style":612},[610,611],[567,1212,1057],{"className":1213,"style":1214},[610,611],"margin-right:0.0715em;",[567,1216,1217,1220],{"style":799},[567,1218],{"className":1219,"style":787},[786],[567,1221],{"className":1222,"style":807},[806],[567,1224],{"className":1225,"style":1123},[1122],[567,1227,1035],{"className":1228},[1127],[567,1230],{"className":1231,"style":1123},[1122],[567,1233,1235,1238],{"className":1234},[601],[567,1236],{"className":1237,"style":763},[605],[567,1239,1241],{"className":1240},[610,767],[567,1242,1244],{"className":1243},[771],[567,1245,1247],{"className":1246},[775],[567,1248,1250,1265],{"className":1249,"style":763},[779],[567,1251,1252,1255],{"style":782},[567,1253],{"className":1254,"style":787},[786],[567,1256,1258,1261],{"className":1257},[610],[567,1259,588],{"className":1260,"style":612},[610,611],[567,1262,1070],{"className":1263,"style":1264},[610,611],"margin-right:0.0278em;",[567,1266,1267,1270],{"style":799},[567,1268],{"className":1269,"style":787},[786],[567,1271],{"className":1272,"style":807},[806],".",[563,1275,1276,1277,1305,1306,1336,1337,1367,1368,1598,1599,1640,1641,1273],{},"Liegt ",[567,1278,1280,1293],{"className":1279},[570],[567,1281,1283],{"className":1282},[574],[576,1284,1285],{"xmlns":578},[580,1286,1287,1291],{},[583,1288,1289],{},[586,1290,588],{},[590,1292,588],{"encoding":592},[567,1294,1296],{"className":1295,"ariaHidden":597},[596],[567,1297,1299,1302],{"className":1298},[601],[567,1300],{"className":1301,"style":606},[605],[567,1303,588],{"className":1304,"style":612},[610,611]," im Abstand ",[567,1307,1309,1323],{"className":1308},[570],[567,1310,1312],{"className":1311},[574],[576,1313,1314],{"xmlns":578},[580,1315,1316,1321],{},[583,1317,1318],{},[586,1319,1320],{},"d",[590,1322,1320],{"encoding":592},[567,1324,1326],{"className":1325,"ariaHidden":597},[596],[567,1327,1329,1333],{"className":1328},[601],[567,1330],{"className":1331,"style":1332},[605],"height:0.6944em;",[567,1334,1320],{"className":1335},[610,611]," vom Mittelpunkt eines Kreises mit Radius ",[567,1338,1340,1354],{"className":1339},[570],[567,1341,1343],{"className":1342},[574],[576,1344,1345],{"xmlns":578},[580,1346,1347,1352],{},[583,1348,1349],{},[586,1350,1351],{},"r",[590,1353,1351],{"encoding":592},[567,1355,1357],{"className":1356,"ariaHidden":597},[596],[567,1358,1360,1364],{"className":1359},[601],[567,1361],{"className":1362,"style":1363},[605],"height:0.4306em;",[567,1365,1351],{"className":1366,"style":1264},[610,611],", gilt ",[567,1369,1371,1423],{"className":1370},[570],[567,1372,1374],{"className":1373},[574],[576,1375,1376],{"xmlns":578},[580,1377,1378,1420],{},[583,1379,1380,1403,1405,1411,1414],{},[1381,1382,1383,1393],"msup",{},[739,1384,1385,1391],{"accent":597},[583,1386,1387,1389],{},[586,1388,588],{},[586,1390,640],{},[748,1392,750],{"stretchy":597},[583,1394,1395,1399],{},[1396,1397,1398],"mtext",{}," ",[1400,1401,1402],"mn",{},"2",[748,1404,1048],{},[1381,1406,1407,1409],{},[586,1408,1320],{},[1400,1410,1402],{},[748,1412,1413],{},"−",[1381,1415,1416,1418],{},[586,1417,1351],{},[1400,1419,1402],{},[590,1421,1422],{"encoding":592},"\\overline{PT}^{\\,2} = d^2 - r^2",[567,1424,1426,1516,1563],{"className":1425,"ariaHidden":597},[596],[567,1427,1429,1433,1507,1510,1513],{"className":1428},[601],[567,1430],{"className":1431,"style":1432},[605],"height:1.0873em;",[567,1434,1436,1470],{"className":1435},[610],[567,1437,1439],{"className":1438},[610,767],[567,1440,1442],{"className":1441},[771],[567,1443,1445],{"className":1444},[775],[567,1446,1448,1462],{"className":1447,"style":763},[779],[567,1449,1450,1453],{"style":782},[567,1451],{"className":1452,"style":787},[786],[567,1454,1456,1459],{"className":1455},[610],[567,1457,588],{"className":1458,"style":612},[610,611],[567,1460,640],{"className":1461,"style":612},[610,611],[567,1463,1464,1467],{"style":799},[567,1465],{"className":1466,"style":787},[786],[567,1468],{"className":1469,"style":807},[806],[567,1471,1474],{"className":1472},[1473],"msupsub",[567,1475,1477],{"className":1476},[771],[567,1478,1480],{"className":1479},[775],[567,1481,1483],{"className":1482,"style":1432},[779],[567,1484,1486,1490],{"style":1485},"top:-3.3362em;margin-right:0.05em;",[567,1487],{"className":1488,"style":1489},[786],"height:2.7em;",[567,1491,1497],{"className":1492},[1493,1494,1495,1496],"sizing","reset-size6","size3","mtight",[567,1498,1500,1504],{"className":1499},[610,1496],[567,1501],{"className":1502,"style":1503},[1122,1496],"margin-right:0.1952em;",[567,1505,1402],{"className":1506},[610,1496],[567,1508],{"className":1509,"style":1174},[1122],[567,1511,1048],{"className":1512},[1178],[567,1514],{"className":1515,"style":1174},[1122],[567,1517,1519,1523,1554,1557,1560],{"className":1518},[601],[567,1520],{"className":1521,"style":1522},[605],"height:0.8974em;vertical-align:-0.0833em;",[567,1524,1526,1529],{"className":1525},[610],[567,1527,1320],{"className":1528},[610,611],[567,1530,1532],{"className":1531},[1473],[567,1533,1535],{"className":1534},[771],[567,1536,1538],{"className":1537},[775],[567,1539,1542],{"className":1540,"style":1541},[779],"height:0.8141em;",[567,1543,1545,1548],{"style":1544},"top:-3.063em;margin-right:0.05em;",[567,1546],{"className":1547,"style":1489},[786],[567,1549,1551],{"className":1550},[1493,1494,1495,1496],[567,1552,1402],{"className":1553},[610,1496],[567,1555],{"className":1556,"style":1123},[1122],[567,1558,1413],{"className":1559},[1127],[567,1561],{"className":1562,"style":1123},[1122],[567,1564,1566,1569],{"className":1565},[601],[567,1567],{"className":1568,"style":1541},[605],[567,1570,1572,1575],{"className":1571},[610],[567,1573,1351],{"className":1574,"style":1264},[610,611],[567,1576,1578],{"className":1577},[1473],[567,1579,1581],{"className":1580},[771],[567,1582,1584],{"className":1583},[775],[567,1585,1587],{"className":1586,"style":1541},[779],[567,1588,1589,1592],{"style":1544},[567,1590],{"className":1591,"style":1489},[786],[567,1593,1595],{"className":1594},[1493,1494,1495,1496],[567,1596,1402],{"className":1597},[610,1496],". Das ist der Satz des Pythagoras im Dreieck ",[567,1600,1602,1621],{"className":1601},[570],[567,1603,1605],{"className":1604},[574],[576,1606,1607],{"xmlns":578},[580,1608,1609,1618],{},[583,1610,1611,1613,1615],{},[586,1612,588],{},[586,1614,640],{},[586,1616,1617],{},"M",[590,1619,1620],{"encoding":592},"PTM",[567,1622,1624],{"className":1623,"ariaHidden":597},[596],[567,1625,1627,1630,1633,1636],{"className":1626},[601],[567,1628],{"className":1629,"style":606},[605],[567,1631,588],{"className":1632,"style":612},[610,611],[567,1634,640],{"className":1635,"style":612},[610,611],[567,1637,1617],{"className":1638,"style":1639},[610,611],"margin-right:0.109em;"," mit dem rechten Winkel bei ",[567,1642,1644,1657],{"className":1643},[570],[567,1645,1647],{"className":1646},[574],[576,1648,1649],{"xmlns":578},[580,1650,1651,1655],{},[583,1652,1653],{},[586,1654,640],{},[590,1656,640],{"encoding":592},[567,1658,1660],{"className":1659,"ariaHidden":597},[596],[567,1661,1663,1666],{"className":1662},[601],[567,1664],{"className":1665,"style":606},[605],[567,1667,640],{"className":1668,"style":612},[610,611],[558,1670,1672],{"id":1671},"herleitung","Herleitung",[563,1674,1675,1676,691,1715,1754,1755,1783,1784,1818,1819,1847],{},"Die Dreiecke ",[567,1677,1679,1697],{"className":1678},[570],[567,1680,1682],{"className":1681},[574],[576,1683,1684],{"xmlns":578},[580,1685,1686,1694],{},[583,1687,1688,1690,1692],{},[586,1689,588],{},[586,1691,640],{},[586,1693,676],{},[590,1695,1696],{"encoding":592},"PTA",[567,1698,1700],{"className":1699,"ariaHidden":597},[596],[567,1701,1703,1706,1709,1712],{"className":1702},[601],[567,1704],{"className":1705,"style":606},[605],[567,1707,588],{"className":1708,"style":612},[610,611],[567,1710,640],{"className":1711,"style":612},[610,611],[567,1713,676],{"className":1714},[610,611],[567,1716,1718,1736],{"className":1717},[570],[567,1719,1721],{"className":1720},[574],[576,1722,1723],{"xmlns":578},[580,1724,1725,1733],{},[583,1726,1727,1729,1731],{},[586,1728,588],{},[586,1730,706],{},[586,1732,640],{},[590,1734,1735],{"encoding":592},"PBT",[567,1737,1739],{"className":1738,"ariaHidden":597},[596],[567,1740,1742,1745,1748,1751],{"className":1741},[601],[567,1743],{"className":1744,"style":606},[605],[567,1746,588],{"className":1747,"style":612},[610,611],[567,1749,706],{"className":1750,"style":721},[610,611],[567,1752,640],{"className":1753,"style":612},[610,611]," sind ähnlich: Sie haben den Winkel bei ",[567,1756,1758,1771],{"className":1757},[570],[567,1759,1761],{"className":1760},[574],[576,1762,1763],{"xmlns":578},[580,1764,1765,1769],{},[583,1766,1767],{},[586,1768,588],{},[590,1770,588],{"encoding":592},[567,1772,1774],{"className":1773,"ariaHidden":597},[596],[567,1775,1777,1780],{"className":1776},[601],[567,1778],{"className":1779,"style":606},[605],[567,1781,588],{"className":1782,"style":612},[610,611]," gemeinsam, und der Winkel zwischen Tangente und Sehne ",[567,1785,1787,1803],{"className":1786},[570],[567,1788,1790],{"className":1789},[574],[576,1791,1792],{"xmlns":578},[580,1793,1794,1800],{},[583,1795,1796,1798],{},[586,1797,640],{},[586,1799,676],{},[590,1801,1802],{"encoding":592},"TA",[567,1804,1806],{"className":1805,"ariaHidden":597},[596],[567,1807,1809,1812,1815],{"className":1808},[601],[567,1810],{"className":1811,"style":606},[605],[567,1813,640],{"className":1814,"style":612},[610,611],[567,1816,676],{"className":1817},[610,611]," ist so groß wie der Umfangswinkel bei ",[567,1820,1822,1835],{"className":1821},[570],[567,1823,1825],{"className":1824},[574],[576,1826,1827],{"xmlns":578},[580,1828,1829,1833],{},[583,1830,1831],{},[586,1832,706],{},[590,1834,706],{"encoding":592},[567,1836,1838],{"className":1837,"ariaHidden":597},[596],[567,1839,1841,1844],{"className":1840},[601],[567,1842],{"className":1843,"style":606},[605],[567,1845,706],{"className":1846,"style":721},[610,611]," über derselben Sehne. Daraus folgt",[567,1849,1852],{"className":1850},[1851],"katex-display",[567,1853,1855,1965],{"className":1854},[570],[567,1856,1858],{"className":1857},[574],[576,1859,1861],{"xmlns":578,"display":1860},"block",[580,1862,1863,1962],{},[583,1864,1865,1888,1890,1912,1915,1918,1920,1938,1940,1950,1952],{},[1866,1867,1868,1878],"mfrac",{},[739,1869,1870,1876],{"accent":597},[583,1871,1872,1874],{},[586,1873,588],{},[586,1875,640],{},[748,1877,750],{"stretchy":597},[739,1879,1880,1886],{"accent":597},[583,1881,1882,1884],{},[586,1883,588],{},[586,1885,676],{},[748,1887,750],{"stretchy":597},[748,1889,1048],{},[1866,1891,1892,1902],{},[739,1893,1894,1900],{"accent":597},[583,1895,1896,1898],{},[586,1897,588],{},[586,1899,706],{},[748,1901,750],{"stretchy":597},[739,1903,1904,1910],{"accent":597},[583,1905,1906,1908],{},[586,1907,588],{},[586,1909,640],{},[748,1911,750],{"stretchy":597},[1122,1913],{"width":1914},"1em",[748,1916,1917],{},"⇒",[1122,1919],{"width":1914},[1381,1921,1922,1932],{},[739,1923,1924,1930],{"accent":597},[583,1925,1926,1928],{},[586,1927,588],{},[586,1929,640],{},[748,1931,750],{"stretchy":597},[583,1933,1934,1936],{},[1396,1935,1398],{},[1400,1937,1402],{},[748,1939,1048],{},[739,1941,1942,1948],{"accent":597},[583,1943,1944,1946],{},[586,1945,588],{},[586,1947,676],{},[748,1949,750],{"stretchy":597},[748,1951,1035],{},[739,1953,1954,1960],{"accent":597},[583,1955,1956,1958],{},[586,1957,588],{},[586,1959,706],{},[748,1961,750],{"stretchy":597},[590,1963,1964],{"encoding":592},"\\frac{\\overline{PT}}{\\overline{PA}} = \\frac{\\overline{PB}}{\\overline{PT}} \\quad\\Rightarrow\\quad \\overline{PT}^{\\,2} = \\overline{PA} \\cdot \\overline{PB}",[567,1966,1968,2120,2266,2347,2396],{"className":1967,"ariaHidden":597},[596],[567,1969,1971,1975,2111,2114,2117],{"className":1970},[601],[567,1972],{"className":1973,"style":1974},[605],"height:2.3337em;vertical-align:-0.7733em;",[567,1976,1978,1983,2107],{"className":1977},[610],[567,1979],{"className":1980},[1981,1982],"mopen","nulldelimiter",[567,1984,1986],{"className":1985},[1866],[567,1987,1990,2098],{"className":1988},[771,1989],"vlist-t2",[567,1991,1993,2093],{"className":1992},[775],[567,1994,1997,2040,2050],{"className":1995,"style":1996},[779],"height:1.5603em;",[567,1998,2000,2003],{"style":1999},"top:-2.2267em;",[567,2001],{"className":2002,"style":787},[786],[567,2004,2006],{"className":2005},[610],[567,2007,2009],{"className":2008},[610,767],[567,2010,2012],{"className":2011},[771],[567,2013,2015],{"className":2014},[775],[567,2016,2018,2032],{"className":2017,"style":763},[779],[567,2019,2020,2023],{"style":782},[567,2021],{"className":2022,"style":787},[786],[567,2024,2026,2029],{"className":2025},[610],[567,2027,588],{"className":2028,"style":612},[610,611],[567,2030,676],{"className":2031},[610,611],[567,2033,2034,2037],{"style":799},[567,2035],{"className":2036,"style":787},[786],[567,2038],{"className":2039,"style":807},[806],[567,2041,2043,2046],{"style":2042},"top:-3.23em;",[567,2044],{"className":2045,"style":787},[786],[567,2047],{"className":2048,"style":807},[2049],"frac-line",[567,2051,2053,2056],{"style":2052},"top:-3.677em;",[567,2054],{"className":2055,"style":787},[786],[567,2057,2059],{"className":2058},[610],[567,2060,2062],{"className":2061},[610,767],[567,2063,2065],{"className":2064},[771],[567,2066,2068],{"className":2067},[775],[567,2069,2071,2085],{"className":2070,"style":763},[779],[567,2072,2073,2076],{"style":782},[567,2074],{"className":2075,"style":787},[786],[567,2077,2079,2082],{"className":2078},[610],[567,2080,588],{"className":2081,"style":612},[610,611],[567,2083,640],{"className":2084,"style":612},[610,611],[567,2086,2087,2090],{"style":799},[567,2088],{"className":2089,"style":787},[786],[567,2091],{"className":2092,"style":807},[806],[567,2094,2097],{"className":2095},[2096],"vlist-s","​",[567,2099,2101],{"className":2100},[775],[567,2102,2105],{"className":2103,"style":2104},[779],"height:0.7733em;",[567,2106],{},[567,2108],{"className":2109},[2110,1982],"mclose",[567,2112],{"className":2113,"style":1174},[1122],[567,2115,1048],{"className":2116},[1178],[567,2118],{"className":2119,"style":1174},[1122],[567,2121,2123,2126,2250,2254,2257,2260,2263],{"className":2122},[601],[567,2124],{"className":2125,"style":1974},[605],[567,2127,2129,2132,2247],{"className":2128},[610],[567,2130],{"className":2131},[1981,1982],[567,2133,2135],{"className":2134},[1866],[567,2136,2138,2239],{"className":2137},[771,1989],[567,2139,2141,2236],{"className":2140},[775],[567,2142,2144,2186,2194],{"className":2143,"style":1996},[779],[567,2145,2146,2149],{"style":1999},[567,2147],{"className":2148,"style":787},[786],[567,2150,2152],{"className":2151},[610],[567,2153,2155],{"className":2154},[610,767],[567,2156,2158],{"className":2157},[771],[567,2159,2161],{"className":2160},[775],[567,2162,2164,2178],{"className":2163,"style":763},[779],[567,2165,2166,2169],{"style":782},[567,2167],{"className":2168,"style":787},[786],[567,2170,2172,2175],{"className":2171},[610],[567,2173,588],{"className":2174,"style":612},[610,611],[567,2176,640],{"className":2177,"style":612},[610,611],[567,2179,2180,2183],{"style":799},[567,2181],{"className":2182,"style":787},[786],[567,2184],{"className":2185,"style":807},[806],[567,2187,2188,2191],{"style":2042},[567,2189],{"className":2190,"style":787},[786],[567,2192],{"className":2193,"style":807},[2049],[567,2195,2196,2199],{"style":2052},[567,2197],{"className":2198,"style":787},[786],[567,2200,2202],{"className":2201},[610],[567,2203,2205],{"className":2204},[610,767],[567,2206,2208],{"className":2207},[771],[567,2209,2211],{"className":2210},[775],[567,2212,2214,2228],{"className":2213,"style":763},[779],[567,2215,2216,2219],{"style":782},[567,2217],{"className":2218,"style":787},[786],[567,2220,2222,2225],{"className":2221},[610],[567,2223,588],{"className":2224,"style":612},[610,611],[567,2226,706],{"className":2227,"style":721},[610,611],[567,2229,2230,2233],{"style":799},[567,2231],{"className":2232,"style":787},[786],[567,2234],{"className":2235,"style":807},[806],[567,2237,2097],{"className":2238},[2096],[567,2240,2242],{"className":2241},[775],[567,2243,2245],{"className":2244,"style":2104},[779],[567,2246],{},[567,2248],{"className":2249},[2110,1982],[567,2251],{"className":2252,"style":2253},[1122],"margin-right:1em;",[567,2255],{"className":2256,"style":1174},[1122],[567,2258,1917],{"className":2259},[1178],[567,2261],{"className":2262,"style":2253},[1122],[567,2264],{"className":2265,"style":1174},[1122],[567,2267,2269,2272,2338,2341,2344],{"className":2268},[601],[567,2270],{"className":2271,"style":1432},[605],[567,2273,2275,2309],{"className":2274},[610],[567,2276,2278],{"className":2277},[610,767],[567,2279,2281],{"className":2280},[771],[567,2282,2284],{"className":2283},[775],[567,2285,2287,2301],{"className":2286,"style":763},[779],[567,2288,2289,2292],{"style":782},[567,2290],{"className":2291,"style":787},[786],[567,2293,2295,2298],{"className":2294},[610],[567,2296,588],{"className":2297,"style":612},[610,611],[567,2299,640],{"className":2300,"style":612},[610,611],[567,2302,2303,2306],{"style":799},[567,2304],{"className":2305,"style":787},[786],[567,2307],{"className":2308,"style":807},[806],[567,2310,2312],{"className":2311},[1473],[567,2313,2315],{"className":2314},[771],[567,2316,2318],{"className":2317},[775],[567,2319,2321],{"className":2320,"style":1432},[779],[567,2322,2323,2326],{"style":1485},[567,2324],{"className":2325,"style":1489},[786],[567,2327,2329],{"className":2328},[1493,1494,1495,1496],[567,2330,2332,2335],{"className":2331},[610,1496],[567,2333],{"className":2334,"style":1503},[1122,1496],[567,2336,1402],{"className":2337},[610,1496],[567,2339],{"className":2340,"style":1174},[1122],[567,2342,1048],{"className":2343},[1178],[567,2345],{"className":2346,"style":1174},[1122],[567,2348,2350,2353,2387,2390,2393],{"className":2349},[601],[567,2351],{"className":2352,"style":763},[605],[567,2354,2356],{"className":2355},[610,767],[567,2357,2359],{"className":2358},[771],[567,2360,2362],{"className":2361},[775],[567,2363,2365,2379],{"className":2364,"style":763},[779],[567,2366,2367,2370],{"style":782},[567,2368],{"className":2369,"style":787},[786],[567,2371,2373,2376],{"className":2372},[610],[567,2374,588],{"className":2375,"style":612},[610,611],[567,2377,676],{"className":2378},[610,611],[567,2380,2381,2384],{"style":799},[567,2382],{"className":2383,"style":787},[786],[567,2385],{"className":2386,"style":807},[806],[567,2388],{"className":2389,"style":1123},[1122],[567,2391,1035],{"className":2392},[1127],[567,2394],{"className":2395,"style":1123},[1122],[567,2397,2399,2402],{"className":2398},[601],[567,2400],{"className":2401,"style":763},[605],[567,2403,2405],{"className":2404},[610,767],[567,2406,2408],{"className":2407},[771],[567,2409,2411],{"className":2410},[775],[567,2412,2414,2428],{"className":2413,"style":763},[779],[567,2415,2416,2419],{"style":782},[567,2417],{"className":2418,"style":787},[786],[567,2420,2422,2425],{"className":2421},[610],[567,2423,588],{"className":2424,"style":612},[610,611],[567,2426,706],{"className":2427,"style":721},[610,611],[567,2429,2430,2433],{"style":799},[567,2431],{"className":2432,"style":787},[786],[567,2434],{"className":2435,"style":807},[806],[558,2437,2439],{"id":2438},"beispiele","Beispiele",[563,2441,2442,2443,2471,2472,2519,2520,2563],{},"Eine Sekante von ",[567,2444,2446,2459],{"className":2445},[570],[567,2447,2449],{"className":2448},[574],[576,2450,2451],{"xmlns":578},[580,2452,2453,2457],{},[583,2454,2455],{},[586,2456,588],{},[590,2458,588],{"encoding":592},[567,2460,2462],{"className":2461,"ariaHidden":597},[596],[567,2463,2465,2468],{"className":2464},[601],[567,2466],{"className":2467,"style":606},[605],[567,2469,588],{"className":2470,"style":612},[610,611]," trifft den Kreis nach ",[567,2473,2475,2495],{"className":2474},[570],[567,2476,2478],{"className":2477},[574],[576,2479,2480],{"xmlns":578},[580,2481,2482,2492],{},[583,2483,2484,2487,2489],{},[1400,2485,2486],{},"4",[1396,2488,1398],{},[1396,2490,2491],{},"cm",[590,2493,2494],{"encoding":592},"4\\,\\text{cm}",[567,2496,2498],{"className":2497,"ariaHidden":597},[596],[567,2499,2501,2505,2508,2512],{"className":2500},[601],[567,2502],{"className":2503,"style":2504},[605],"height:0.6444em;",[567,2506,2486],{"className":2507},[610],[567,2509],{"className":2510,"style":2511},[1122],"margin-right:0.1667em;",[567,2513,2516],{"className":2514},[610,2515],"text",[567,2517,2491],{"className":2518},[610]," und verlässt ihn nach ",[567,2521,2523,2542],{"className":2522},[570],[567,2524,2526],{"className":2525},[574],[576,2527,2528],{"xmlns":578},[580,2529,2530,2539],{},[583,2531,2532,2535,2537],{},[1400,2533,2534],{},"9",[1396,2536,1398],{},[1396,2538,2491],{},[590,2540,2541],{"encoding":592},"9\\,\\text{cm}",[567,2543,2545],{"className":2544,"ariaHidden":597},[596],[567,2546,2548,2551,2554,2557],{"className":2547},[601],[567,2549],{"className":2550,"style":2504},[605],[567,2552,2534],{"className":2553},[610],[567,2555],{"className":2556,"style":2511},[1122],[567,2558,2560],{"className":2559},[610,2515],[567,2561,2491],{"className":2562},[610],". Der Tangentenabschnitt ist",[567,2565,2567],{"className":2566},[1851],[567,2568,2570,2614],{"className":2569},[570],[567,2571,2573],{"className":2572},[574],[576,2574,2575],{"xmlns":578,"display":1860},[580,2576,2577,2611],{},[583,2578,2579,2589,2591,2602,2604,2607,2609],{},[739,2580,2581,2587],{"accent":597},[583,2582,2583,2585],{},[586,2584,588],{},[586,2586,640],{},[748,2588,750],{"stretchy":597},[748,2590,1048],{},[2592,2593,2594],"msqrt",{},[583,2595,2596,2598,2600],{},[1400,2597,2486],{},[748,2599,1035],{},[1400,2601,2534],{},[748,2603,1048],{},[1400,2605,2606],{},"6",[1396,2608,1398],{},[1396,2610,2491],{},[590,2612,2613],{"encoding":592},"\\overline{PT} = \\sqrt{4 \\cdot 9} = 6\\,\\text{cm}",[567,2615,2617,2666,2757],{"className":2616,"ariaHidden":597},[596],[567,2618,2620,2623,2657,2660,2663],{"className":2619},[601],[567,2621],{"className":2622,"style":763},[605],[567,2624,2626],{"className":2625},[610,767],[567,2627,2629],{"className":2628},[771],[567,2630,2632],{"className":2631},[775],[567,2633,2635,2649],{"className":2634,"style":763},[779],[567,2636,2637,2640],{"style":782},[567,2638],{"className":2639,"style":787},[786],[567,2641,2643,2646],{"className":2642},[610],[567,2644,588],{"className":2645,"style":612},[610,611],[567,2647,640],{"className":2648,"style":612},[610,611],[567,2650,2651,2654],{"style":799},[567,2652],{"className":2653,"style":787},[786],[567,2655],{"className":2656,"style":807},[806],[567,2658],{"className":2659,"style":1174},[1122],[567,2661,1048],{"className":2662},[1178],[567,2664],{"className":2665,"style":1174},[1122],[567,2667,2669,2673,2748,2751,2754],{"className":2668},[601],[567,2670],{"className":2671,"style":2672},[605],"height:1.04em;vertical-align:-0.0839em;",[567,2674,2677],{"className":2675},[610,2676],"sqrt",[567,2678,2680,2739],{"className":2679},[771,1989],[567,2681,2683,2736],{"className":2682},[775],[567,2684,2687,2713],{"className":2685,"style":2686},[779],"height:0.9561em;",[567,2688,2691,2694],{"className":2689,"style":782},[2690],"svg-align",[567,2692],{"className":2693,"style":787},[786],[567,2695,2698,2701,2704,2707,2710],{"className":2696,"style":2697},[610],"padding-left:0.833em;",[567,2699,2486],{"className":2700},[610],[567,2702],{"className":2703,"style":1123},[1122],[567,2705,1035],{"className":2706},[1127],[567,2708],{"className":2709,"style":1123},[1122],[567,2711,2534],{"className":2712},[610],[567,2714,2716,2719],{"style":2715},"top:-2.9161em;",[567,2717],{"className":2718,"style":787},[786],[567,2720,2724],{"className":2721,"style":2723},[2722],"hide-tail","min-width:0.853em;height:1.08em;",[2725,2726,2732],"svg",{"xmlns":2727,"width":2728,"height":2729,"viewBox":2730,"preserveAspectRatio":2731},"http:\u002F\u002Fwww.w3.org\u002F2000\u002Fsvg","400em","1.08em","0 0 400000 1080","xMinYMin slice",[2733,2734],"path",{"d":2735},"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 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",[567,2779,2781,2795],{"className":2780},[570],[567,2782,2784],{"className":2783},[574],[576,2785,2786],{"xmlns":578},[580,2787,2788,2793],{},[583,2789,2790],{},[1400,2791,2792],{},"5",[590,2794,2792],{"encoding":592},[567,2796,2798],{"className":2797,"ariaHidden":597},[596],[567,2799,2801,2804],{"className":2800},[601],[567,2802],{"className":2803,"style":2504},[605],[567,2805,2792],{"className":2806},[610]," um den Ursprung, ",[567,2809,2811,2841],{"className":2810},[570],[567,2812,2814],{"className":2813},[574],[576,2815,2816],{"xmlns":578},[580,2817,2818,2838],{},[583,2819,2820,2822,2826,2829,2832,2835],{},[586,2821,588],{},[748,2823,2825],{"stretchy":2824},"false","(",[1400,2827,2828],{},"13",[748,2830,2831],{},"∣",[1400,2833,2834],{},"0",[748,2836,2837],{"stretchy":2824},")",[590,2839,2840],{"encoding":592},"P(13 \\mid 0)",[567,2842,2844,2869],{"className":2843,"ariaHidden":597},[596],[567,2845,2847,2851,2854,2857,2860,2863,2866],{"className":2846},[601],[567,2848],{"className":2849,"style":2850},[605],"height:1em;vertical-align:-0.25em;",[567,2852,588],{"className":2853,"style":612},[610,611],[567,2855,2825],{"className":2856},[1981],[567,2858,2828],{"className":2859},[610],[567,2861],{"className":2862,"style":1174},[1122],[567,2864,2831],{"className":2865},[1178],[567,2867],{"className":2868,"style":1174},[1122],[567,2870,2872,2875,2878],{"className":2871},[601],[567,2873],{"className":2874,"style":2850},[605],[567,2876,2834],{"className":2877},[610],[567,2879,2837],{"className":2880},[2110],". Die Sekante entlang der x-Achse trifft den Kreis bei ",[567,2883,2885,2904],{"className":2884},[570],[567,2886,2888],{"className":2887},[574],[576,2889,2890],{"xmlns":578},[580,2891,2892,2901],{},[583,2893,2894,2897,2899],{},[586,2895,2896],{},"x",[748,2898,1048],{},[1400,2900,2792],{},[590,2902,2903],{"encoding":592},"x = 5",[567,2905,2907,2925],{"className":2906,"ariaHidden":597},[596],[567,2908,2910,2913,2916,2919,2922],{"className":2909},[601],[567,2911],{"className":2912,"style":1363},[605],[567,2914,2896],{"className":2915},[610,611],[567,2917],{"className":2918,"style":1174},[1122],[567,2920,1048],{"className":2921},[1178],[567,2923],{"className":2924,"style":1174},[1122],[567,2926,2928,2931],{"className":2927},[601],[567,2929],{"className":2930,"style":2504},[605],[567,2932,2792],{"className":2933},[610],[567,2935,2937,2957],{"className":2936},[570],[567,2938,2940],{"className":2939},[574],[576,2941,2942],{"xmlns":578},[580,2943,2944,2954],{},[583,2945,2946,2948,2950,2952],{},[586,2947,2896],{},[748,2949,1048],{},[748,2951,1413],{},[1400,2953,2792],{},[590,2955,2956],{"encoding":592},"x = -5",[567,2958,2960,2978],{"className":2959,"ariaHidden":597},[596],[567,2961,2963,2966,2969,2972,2975],{"className":2962},[601],[567,2964],{"className":2965,"style":1363},[605],[567,2967,2896],{"className":2968},[610,611],[567,2970],{"className":2971,"style":1174},[1122],[567,2973,1048],{"className":2974},[1178],[567,2976],{"className":2977,"style":1174},[1122],[567,2979,2981,2985,2988],{"className":2980},[601],[567,2982],{"className":2983,"style":2984},[605],"height:0.7278em;vertical-align:-0.0833em;",[567,2986,1413],{"className":2987},[610],[567,2989,2792],{"className":2990},[610],", also ",[567,2993,2995,3022],{"className":2994},[570],[567,2996,2998],{"className":2997},[574],[576,2999,3000],{"xmlns":578},[580,3001,3002,3019],{},[583,3003,3004,3014,3016],{},[739,3005,3006,3012],{"accent":597},[583,3007,3008,3010],{},[586,3009,588],{},[586,3011,676],{},[748,3013,750],{"stretchy":597},[748,3015,1048],{},[1400,3017,3018],{},"8",[590,3020,3021],{"encoding":592},"\\overline{PA} = 8",[567,3023,3025,3074],{"className":3024,"ariaHidden":597},[596],[567,3026,3028,3031,3065,3068,3071],{"className":3027},[601],[567,3029],{"className":3030,"style":763},[605],[567,3032,3034],{"className":3033},[610,767],[567,3035,3037],{"className":3036},[771],[567,3038,3040],{"className":3039},[775],[567,3041,3043,3057],{"className":3042,"style":763},[779],[567,3044,3045,3048],{"style":782},[567,3046],{"className":3047,"style":787},[786],[567,3049,3051,3054],{"className":3050},[610],[567,3052,588],{"className":3053,"style":612},[610,611],[567,3055,676],{"className":3056},[610,611],[567,3058,3059,3062],{"style":799},[567,3060],{"className":3061,"style":787},[786],[567,3063],{"className":3064,"style":807},[806],[567,3066],{"className":3067,"style":1174},[1122],[567,3069,1048],{"className":3070},[1178],[567,3072],{"className":3073,"style":1174},[1122],[567,3075,3077,3080],{"className":3076},[601],[567,3078],{"className":3079,"style":2504},[605],[567,3081,3018],{"className":3082},[610],[567,3084,3086,3113],{"className":3085},[570],[567,3087,3089],{"className":3088},[574],[576,3090,3091],{"xmlns":578},[580,3092,3093,3110],{},[583,3094,3095,3105,3107],{},[739,3096,3097,3103],{"accent":597},[583,3098,3099,3101],{},[586,3100,588],{},[586,3102,706],{},[748,3104,750],{"stretchy":597},[748,3106,1048],{},[1400,3108,3109],{},"18",[590,3111,3112],{"encoding":592},"\\overline{PB} = 18",[567,3114,3116,3165],{"className":3115,"ariaHidden":597},[596],[567,3117,3119,3122,3156,3159,3162],{"className":3118},[601],[567,3120],{"className":3121,"style":763},[605],[567,3123,3125],{"className":3124},[610,767],[567,3126,3128],{"className":3127},[771],[567,3129,3131],{"className":3130},[775],[567,3132,3134,3148],{"className":3133,"style":763},[779],[567,3135,3136,3139],{"style":782},[567,3137],{"className":3138,"style":787},[786],[567,3140,3142,3145],{"className":3141},[610],[567,3143,588],{"className":3144,"style":612},[610,611],[567,3146,706],{"className":3147,"style":721},[610,611],[567,3149,3150,3153],{"style":799},[567,3151],{"className":3152,"style":787},[786],[567,3154],{"className":3155,"style":807},[806],[567,3157],{"className":3158,"style":1174},[1122],[567,3160,1048],{"className":3161},[1178],[567,3163],{"className":3164,"style":1174},[1122],[567,3166,3168,3171],{"className":3167},[601],[567,3169],{"className":3170,"style":2504},[605],[567,3172,3109],{"className":3173},[610],":",[567,3176,3178],{"className":3177},[1851],[567,3179,3181,3253],{"className":3180},[570],[567,3182,3184],{"className":3183},[574],[576,3185,3186],{"xmlns":578,"display":1860},[580,3187,3188,3250],{},[583,3189,3190,3192,3194,3196,3198,3201,3203,3210,3213,3216,3226,3228,3246,3248],{},[1400,3191,3018],{},[748,3193,1035],{},[1400,3195,3109],{},[748,3197,1048],{},[1400,3199,3200],{},"144",[748,3202,1048],{},[1381,3204,3205,3208],{},[1400,3206,3207],{},"12",[1400,3209,1402],{},[748,3211,3212],{"separator":597},",",[1122,3214],{"width":3215},"2em",[739,3217,3218,3224],{"accent":597},[583,3219,3220,3222],{},[586,3221,588],{},[586,3223,640],{},[748,3225,750],{"stretchy":597},[748,3227,1048],{},[2592,3229,3230],{},[583,3231,3232,3238,3240],{},[1381,3233,3234,3236],{},[1400,3235,2828],{},[1400,3237,1402],{},[748,3239,1413],{},[1381,3241,3242,3244],{},[1400,3243,2792],{},[1400,3245,1402],{},[748,3247,1048],{},[1400,3249,3207],{},[590,3251,3252],{"encoding":592},"8 \\cdot 18 = 144 = 12^2, \\qquad \\overline{PT} = \\sqrt{13^2 - 5^2} = 12",[567,3254,3256,3274,3292,3310,3406,3549],{"className":3255,"ariaHidden":597},[596],[567,3257,3259,3262,3265,3268,3271],{"className":3258},[601],[567,3260],{"className":3261,"style":2504},[605],[567,3263,3018],{"className":3264},[610],[567,3266],{"className":3267,"style":1123},[1122],[567,3269,1035],{"className":3270},[1127],[567,3272],{"className":3273,"style":1123},[1122],[567,3275,3277,3280,3283,3286,3289],{"className":3276},[601],[567,3278],{"className":3279,"style":2504},[605],[567,3281,3109],{"className":3282},[610],[567,3284],{"className":3285,"style":1174},[1122],[567,3287,1048],{"className":3288},[1178],[567,3290],{"className":3291,"style":1174},[1122],[567,3293,3295,3298,3301,3304,3307],{"className":3294},[601],[567,3296],{"className":3297,"style":2504},[605],[567,3299,3200],{"className":3300},[610],[567,3302],{"className":3303,"style":1174},[1122],[567,3305,1048],{"className":3306},[1178],[567,3308],{"className":3309,"style":1174},[1122],[567,3311,3313,3317,3321,3352,3356,3360,3363,3397,3400,3403],{"className":3312},[601],[567,3314],{"className":3315,"style":3316},[605],"height:1.0778em;vertical-align:-0.1944em;",[567,3318,3320],{"className":3319},[610],"1",[567,3322,3324,3327],{"className":3323},[610],[567,3325,1402],{"className":3326},[610],[567,3328,3330],{"className":3329},[1473],[567,3331,3333],{"className":3332},[771],[567,3334,3336],{"className":3335},[775],[567,3337,3340],{"className":3338,"style":3339},[779],"height:0.8641em;",[567,3341,3343,3346],{"style":3342},"top:-3.113em;margin-right:0.05em;",[567,3344],{"className":3345,"style":1489},[786],[567,3347,3349],{"className":3348},[1493,1494,1495,1496],[567,3350,1402],{"className":3351},[610,1496],[567,3353,3212],{"className":3354},[3355],"mpunct",[567,3357],{"className":3358,"style":3359},[1122],"margin-right:2em;",[567,3361],{"className":3362,"style":2511},[1122],[567,3364,3366],{"className":3365},[610,767],[567,3367,3369],{"className":3368},[771],[567,3370,3372],{"className":3371},[775],[567,3373,3375,3389],{"className":3374,"style":763},[779],[567,3376,3377,3380],{"style":782},[567,3378],{"className":3379,"style":787},[786],[567,3381,3383,3386],{"className":3382},[610],[567,3384,588],{"className":3385,"style":612},[610,611],[567,3387,640],{"className":3388,"style":612},[610,611],[567,3390,3391,3394],{"style":799},[567,3392],{"className":3393,"style":787},[786],[567,3395],{"className":3396,"style":807},[806],[567,3398],{"className":3399,"style":1174},[1122],[567,3401,1048],{"className":3402},[1178],[567,3404],{"className":3405,"style":1174},[1122],[567,3407,3409,3413,3540,3543,3546],{"className":3408},[601],[567,3410],{"className":3411,"style":3412},[605],"height:1.24em;vertical-align:-0.1777em;",[567,3414,3416],{"className":3415},[610,2676],[567,3417,3419,3531],{"className":3418},[771,1989],[567,3420,3422,3528],{"className":3421},[775],[567,3423,3426,3511],{"className":3424,"style":3425},[779],"height:1.0623em;",[567,3427,3430,3434],{"className":3428,"style":3429},[2690],"top:-3.2em;",[567,3431],{"className":3432,"style":3433},[786],"height:3.2em;",[567,3435,3438,3441,3473,3476,3479,3482],{"className":3436,"style":3437},[610],"padding-left:1em;",[567,3439,3320],{"className":3440},[610],[567,3442,3444,3448],{"className":3443},[610],[567,3445,3447],{"className":3446},[610],"3",[567,3449,3451],{"className":3450},[1473],[567,3452,3454],{"className":3453},[771],[567,3455,3457],{"className":3456},[775],[567,3458,3461],{"className":3459,"style":3460},[779],"height:0.7401em;",[567,3462,3464,3467],{"style":3463},"top:-2.989em;margin-right:0.05em;",[567,3465],{"className":3466,"style":1489},[786],[567,3468,3470],{"className":3469},[1493,1494,1495,1496],[567,3471,1402],{"className":3472},[610,1496],[567,3474],{"className":3475,"style":1123},[1122],[567,3477,1413],{"className":3478},[1127],[567,3480],{"className":3481,"style":1123},[1122],[567,3483,3485,3488],{"className":3484},[610],[567,3486,2792],{"className":3487},[610],[567,3489,3491],{"className":3490},[1473],[567,3492,3494],{"className":3493},[771],[567,3495,3497],{"className":3496},[775],[567,3498,3500],{"className":3499,"style":3460},[779],[567,3501,3502,3505],{"style":3463},[567,3503],{"className":3504,"style":1489},[786],[567,3506,3508],{"className":3507},[1493,1494,1495,1496],[567,3509,1402],{"className":3510},[610,1496],[567,3512,3514,3517],{"style":3513},"top:-3.0223em;",[567,3515],{"className":3516,"style":3433},[786],[567,3518,3521],{"className":3519,"style":3520},[2722],"min-width:1.02em;height:1.28em;",[2725,3522,3525],{"xmlns":2727,"width":2728,"height":3523,"viewBox":3524,"preserveAspectRatio":2731},"1.28em","0 0 400000 1296",[2733,3526],{"d":3527},"M263,681c0.7,0,18,39.7,52,119\nc34,79.3,68.167,158.7,102.5,238c34.3,79.3,51.8,119.3,52.5,120\nc340,-704.7,510.7,-1060.3,512,-1067\nl0 -0\nc4.7,-7.3,11,-11,19,-11\nH40000v40H1012.3\ns-271.3,567,-271.3,567c-38.7,80.7,-84,175,-136,283c-52,108,-89.167,185.3,-111.5,232\nc-22.3,46.7,-33.8,70.3,-34.5,71c-4.7,4.7,-12.3,7,-23,7s-12,-1,-12,-1\ns-109,-253,-109,-253c-72.7,-168,-109.3,-252,-110,-252c-10.7,8,-22,16.7,-34,26\nc-22,17.3,-33.3,26,-34,26s-26,-26,-26,-26s76,-59,76,-59s76,-60,76,-60z\nM1001 80h400000v40h-400000z",[567,3529,2097],{"className":3530},[2096],[567,3532,3534],{"className":3533},[775],[567,3535,3538],{"className":3536,"style":3537},[779],"height:0.1777em;",[567,3539],{},[567,3541],{"className":3542,"style":1174},[1122],[567,3544,1048],{"className":3545},[1178],[567,3547],{"className":3548,"style":1174},[1122],[567,3550,3552,3555],{"className":3551},[601],[567,3553],{"className":3554,"style":2504},[605],[567,3556,3207],{"className":3557},[610],[563,3559,3560,3561,3603,3604,3646,3647,3847,3848,3934],{},"Der Tangentenabschnitt ist ",[567,3562,3564,3582],{"className":3563},[570],[567,3565,3567],{"className":3566},[574],[576,3568,3569],{"xmlns":578},[580,3570,3571,3579],{},[583,3572,3573,3575,3577],{},[1400,3574,2606],{},[1396,3576,1398],{},[1396,3578,2491],{},[590,3580,3581],{"encoding":592},"6\\,\\text{cm}",[567,3583,3585],{"className":3584,"ariaHidden":597},[596],[567,3586,3588,3591,3594,3597],{"className":3587},[601],[567,3589],{"className":3590,"style":2504},[605],[567,3592,2606],{"className":3593},[610],[567,3595],{"className":3596,"style":2511},[1122],[567,3598,3600],{"className":3599},[610,2515],[567,3601,2491],{"className":3602},[610],", der kurze Sekantenabschnitt ",[567,3605,3607,3625],{"className":3606},[570],[567,3608,3610],{"className":3609},[574],[576,3611,3612],{"xmlns":578},[580,3613,3614,3622],{},[583,3615,3616,3618,3620],{},[1400,3617,3447],{},[1396,3619,1398],{},[1396,3621,2491],{},[590,3623,3624],{"encoding":592},"3\\,\\text{cm}",[567,3626,3628],{"className":3627,"ariaHidden":597},[596],[567,3629,3631,3634,3637,3640],{"className":3630},[601],[567,3632],{"className":3633,"style":2504},[605],[567,3635,3447],{"className":3636},[610],[567,3638],{"className":3639,"style":2511},[1122],[567,3641,3643],{"className":3642},[610,2515],[567,3644,2491],{"className":3645},[610],". Dann ist ",[567,3648,3650,3689],{"className":3649},[570],[567,3651,3653],{"className":3652},[574],[576,3654,3655],{"xmlns":578},[580,3656,3657,3686],{},[583,3658,3659,3669,3671,3678,3680,3682,3684],{},[739,3660,3661,3667],{"accent":597},[583,3662,3663,3665],{},[586,3664,588],{},[586,3666,706],{},[748,3668,750],{"stretchy":597},[748,3670,1048],{},[1866,3672,3673,3676],{},[1400,3674,3675],{},"36",[1400,3677,3447],{},[748,3679,1048],{},[1400,3681,3207],{},[1396,3683,1398],{},[1396,3685,2491],{},[590,3687,3688],{"encoding":592},"\\overline{PB} = \\frac{36}{3} = 12\\,\\text{cm}",[567,3690,3692,3741,3829],{"className":3691,"ariaHidden":597},[596],[567,3693,3695,3698,3732,3735,3738],{"className":3694},[601],[567,3696],{"className":3697,"style":763},[605],[567,3699,3701],{"className":3700},[610,767],[567,3702,3704],{"className":3703},[771],[567,3705,3707],{"className":3706},[775],[567,3708,3710,3724],{"className":3709,"style":763},[779],[567,3711,3712,3715],{"style":782},[567,3713],{"className":3714,"style":787},[786],[567,3716,3718,3721],{"className":3717},[610],[567,3719,588],{"className":3720,"style":612},[610,611],[567,3722,706],{"className":3723,"style":721},[610,611],[567,3725,3726,3729],{"style":799},[567,3727],{"className":3728,"style":787},[786],[567,3730],{"className":3731,"style":807},[806],[567,3733],{"className":3734,"style":1174},[1122],[567,3736,1048],{"className":3737},[1178],[567,3739],{"className":3740,"style":1174},[1122],[567,3742,3744,3748,3820,3823,3826],{"className":3743},[601],[567,3745],{"className":3746,"style":3747},[605],"height:1.1901em;vertical-align:-0.345em;",[567,3749,3751,3754,3817],{"className":3750},[610],[567,3752],{"className":3753},[1981,1982],[567,3755,3757],{"className":3756},[1866],[567,3758,3760,3808],{"className":3759},[771,1989],[567,3761,3763,3805],{"className":3762},[775],[567,3764,3767,3782,3790],{"className":3765,"style":3766},[779],"height:0.8451em;",[567,3768,3770,3773],{"style":3769},"top:-2.655em;",[567,3771],{"className":3772,"style":787},[786],[567,3774,3776],{"className":3775},[1493,1494,1495,1496],[567,3777,3779],{"className":3778},[610,1496],[567,3780,3447],{"className":3781},[610,1496],[567,3783,3784,3787],{"style":2042},[567,3785],{"className":3786,"style":787},[786],[567,3788],{"className":3789,"style":807},[2049],[567,3791,3793,3796],{"style":3792},"top:-3.394em;",[567,3794],{"className":3795,"style":787},[786],[567,3797,3799],{"className":3798},[1493,1494,1495,1496],[567,3800,3802],{"className":3801},[610,1496],[567,3803,3675],{"className":3804},[610,1496],[567,3806,2097],{"className":3807},[2096],[567,3809,3811],{"className":3810},[775],[567,3812,3815],{"className":3813,"style":3814},[779],"height:0.345em;",[567,3816],{},[567,3818],{"className":3819},[2110,1982],[567,3821],{"className":3822,"style":1174},[1122],[567,3824,1048],{"className":3825},[1178],[567,3827],{"className":3828,"style":1174},[1122],[567,3830,3832,3835,3838,3841],{"className":3831},[601],[567,3833],{"className":3834,"style":2504},[605],[567,3836,3207],{"className":3837},[610],[567,3839],{"className":3840,"style":2511},[1122],[567,3842,3844],{"className":3843},[610,2515],[567,3845,2491],{"className":3846},[610],", die Sehne im Kreis also ",[567,3849,3851,3877],{"className":3850},[570],[567,3852,3854],{"className":3853},[574],[576,3855,3856],{"xmlns":578},[580,3857,3858,3874],{},[583,3859,3860,3862,3864,3866,3868,3870,3872],{},[1400,3861,3207],{},[748,3863,1413],{},[1400,3865,3447],{},[748,3867,1048],{},[1400,3869,2534],{},[1396,3871,1398],{},[1396,3873,2491],{},[590,3875,3876],{"encoding":592},"12 - 3 = 9\\,\\text{cm}",[567,3878,3880,3898,3916],{"className":3879,"ariaHidden":597},[596],[567,3881,3883,3886,3889,3892,3895],{"className":3882},[601],[567,3884],{"className":3885,"style":2984},[605],[567,3887,3207],{"className":3888},[610],[567,3890],{"className":3891,"style":1123},[1122],[567,3893,1413],{"className":3894},[1127],[567,3896],{"className":3897,"style":1123},[1122],[567,3899,3901,3904,3907,3910,3913],{"className":3900},[601],[567,3902],{"className":3903,"style":2504},[605],[567,3905,3447],{"className":3906},[610],[567,3908],{"className":3909,"style":1174},[1122],[567,3911,1048],{"className":3912},[1178],[567,3914],{"className":3915,"style":1174},[1122],[567,3917,3919,3922,3925,3928],{"className":3918},[601],[567,3920],{"className":3921,"style":2504},[605],[567,3923,2534],{"className":3924},[610],[567,3926],{"className":3927,"style":2511},[1122],[567,3929,3931],{"className":3930},[610,2515],[567,3932,2491],{"className":3933},[610]," lang.",[558,3936,3938],{"id":3937},"typische-fehler","Typische Fehler",[615,3940,3941,4178,4402],{},[618,3942,3943,3944,4011,4012,4080,4081,4148,4149,4177],{},"Für ",[567,3945,3947,3968],{"className":3946},[570],[567,3948,3950],{"className":3949},[574],[576,3951,3952],{"xmlns":578},[580,3953,3954,3966],{},[583,3955,3956],{},[739,3957,3958,3964],{"accent":597},[583,3959,3960,3962],{},[586,3961,588],{},[586,3963,706],{},[748,3965,750],{"stretchy":597},[590,3967,902],{"encoding":592},[567,3969,3971],{"className":3970,"ariaHidden":597},[596],[567,3972,3974,3977],{"className":3973},[601],[567,3975],{"className":3976,"style":763},[605],[567,3978,3980],{"className":3979},[610,767],[567,3981,3983],{"className":3982},[771],[567,3984,3986],{"className":3985},[775],[567,3987,3989,4003],{"className":3988,"style":763},[779],[567,3990,3991,3994],{"style":782},[567,3992],{"className":3993,"style":787},[786],[567,3995,3997,4000],{"className":3996},[610],[567,3998,588],{"className":3999,"style":612},[610,611],[567,4001,706],{"className":4002,"style":721},[610,611],[567,4004,4005,4008],{"style":799},[567,4006],{"className":4007,"style":787},[786],[567,4009],{"className":4010,"style":807},[806]," nur die Sehne ",[567,4013,4015,4037],{"className":4014},[570],[567,4016,4018],{"className":4017},[574],[576,4019,4020],{"xmlns":578},[580,4021,4022,4034],{},[583,4023,4024],{},[739,4025,4026,4032],{"accent":597},[583,4027,4028,4030],{},[586,4029,676],{},[586,4031,706],{},[748,4033,750],{"stretchy":597},[590,4035,4036],{"encoding":592},"\\overline{AB}",[567,4038,4040],{"className":4039,"ariaHidden":597},[596],[567,4041,4043,4046],{"className":4042},[601],[567,4044],{"className":4045,"style":763},[605],[567,4047,4049],{"className":4048},[610,767],[567,4050,4052],{"className":4051},[771],[567,4053,4055],{"className":4054},[775],[567,4056,4058,4072],{"className":4057,"style":763},[779],[567,4059,4060,4063],{"style":782},[567,4061],{"className":4062,"style":787},[786],[567,4064,4066,4069],{"className":4065},[610],[567,4067,676],{"className":4068},[610,611],[567,4070,706],{"className":4071,"style":721},[610,611],[567,4073,4074,4077],{"style":799},[567,4075],{"className":4076,"style":787},[786],[567,4078],{"className":4079,"style":807},[806]," einsetzen. ",[567,4082,4084,4105],{"className":4083},[570],[567,4085,4087],{"className":4086},[574],[576,4088,4089],{"xmlns":578},[580,4090,4091,4103],{},[583,4092,4093],{},[739,4094,4095,4101],{"accent":597},[583,4096,4097,4099],{},[586,4098,588],{},[586,4100,706],{},[748,4102,750],{"stretchy":597},[590,4104,902],{"encoding":592},[567,4106,4108],{"className":4107,"ariaHidden":597},[596],[567,4109,4111,4114],{"className":4110},[601],[567,4112],{"className":4113,"style":763},[605],[567,4115,4117],{"className":4116},[610,767],[567,4118,4120],{"className":4119},[771],[567,4121,4123],{"className":4122},[775],[567,4124,4126,4140],{"className":4125,"style":763},[779],[567,4127,4128,4131],{"style":782},[567,4129],{"className":4130,"style":787},[786],[567,4132,4134,4137],{"className":4133},[610],[567,4135,588],{"className":4136,"style":612},[610,611],[567,4138,706],{"className":4139,"style":721},[610,611],[567,4141,4142,4145],{"style":799},[567,4143],{"className":4144,"style":787},[786],[567,4146],{"className":4147,"style":807},[806]," ist der ganze Weg von ",[567,4150,4152,4165],{"className":4151},[570],[567,4153,4155],{"className":4154},[574],[576,4156,4157],{"xmlns":578},[580,4158,4159,4163],{},[583,4160,4161],{},[586,4162,588],{},[590,4164,588],{"encoding":592},[567,4166,4168],{"className":4167,"ariaHidden":597},[596],[567,4169,4171,4174],{"className":4170},[601],[567,4172],{"className":4173,"style":606},[605],[567,4175,588],{"className":4176,"style":612},[610,611]," bis zum zweiten Schnittpunkt.",[618,4179,4180,4181,4311,4312,1273],{},"Die Wurzel am Ende vergessen: ",[567,4182,4184,4218],{"className":4183},[570],[567,4185,4187],{"className":4186},[574],[576,4188,4189],{"xmlns":578},[580,4190,4191,4215],{},[583,4192,4193,4211,4213],{},[1381,4194,4195,4205],{},[739,4196,4197,4203],{"accent":597},[583,4198,4199,4201],{},[586,4200,588],{},[586,4202,640],{},[748,4204,750],{"stretchy":597},[583,4206,4207,4209],{},[1396,4208,1398],{},[1400,4210,1402],{},[748,4212,1048],{},[1400,4214,3675],{},[590,4216,4217],{"encoding":592},"\\overline{PT}^{\\,2} = 36",[567,4219,4221,4302],{"className":4220,"ariaHidden":597},[596],[567,4222,4224,4227,4293,4296,4299],{"className":4223},[601],[567,4225],{"className":4226,"style":1432},[605],[567,4228,4230,4264],{"className":4229},[610],[567,4231,4233],{"className":4232},[610,767],[567,4234,4236],{"className":4235},[771],[567,4237,4239],{"className":4238},[775],[567,4240,4242,4256],{"className":4241,"style":763},[779],[567,4243,4244,4247],{"style":782},[567,4245],{"className":4246,"style":787},[786],[567,4248,4250,4253],{"className":4249},[610],[567,4251,588],{"className":4252,"style":612},[610,611],[567,4254,640],{"className":4255,"style":612},[610,611],[567,4257,4258,4261],{"style":799},[567,4259],{"className":4260,"style":787},[786],[567,4262],{"className":4263,"style":807},[806],[567,4265,4267],{"className":4266},[1473],[567,4268,4270],{"className":4269},[771],[567,4271,4273],{"className":4272},[775],[567,4274,4276],{"className":4275,"style":1432},[779],[567,4277,4278,4281],{"style":1485},[567,4279],{"className":4280,"style":1489},[786],[567,4282,4284],{"className":4283},[1493,1494,1495,1496],[567,4285,4287,4290],{"className":4286},[610,1496],[567,4288],{"className":4289,"style":1503},[1122,1496],[567,4291,1402],{"className":4292},[610,1496],[567,4294],{"className":4295,"style":1174},[1122],[567,4297,1048],{"className":4298},[1178],[567,4300],{"className":4301,"style":1174},[1122],[567,4303,4305,4308],{"className":4304},[601],[567,4306],{"className":4307,"style":2504},[605],[567,4309,3675],{"className":4310},[610]," heißt ",[567,4313,4315,4341],{"className":4314},[570],[567,4316,4318],{"className":4317},[574],[576,4319,4320],{"xmlns":578},[580,4321,4322,4338],{},[583,4323,4324,4334,4336],{},[739,4325,4326,4332],{"accent":597},[583,4327,4328,4330],{},[586,4329,588],{},[586,4331,640],{},[748,4333,750],{"stretchy":597},[748,4335,1048],{},[1400,4337,2606],{},[590,4339,4340],{"encoding":592},"\\overline{PT} = 6",[567,4342,4344,4393],{"className":4343,"ariaHidden":597},[596],[567,4345,4347,4350,4384,4387,4390],{"className":4346},[601],[567,4348],{"className":4349,"style":763},[605],[567,4351,4353],{"className":4352},[610,767],[567,4354,4356],{"className":4355},[771],[567,4357,4359],{"className":4358},[775],[567,4360,4362,4376],{"className":4361,"style":763},[779],[567,4363,4364,4367],{"style":782},[567,4365],{"className":4366,"style":787},[786],[567,4368,4370,4373],{"className":4369},[610],[567,4371,588],{"className":4372,"style":612},[610,611],[567,4374,640],{"className":4375,"style":612},[610,611],[567,4377,4378,4381],{"style":799},[567,4379],{"className":4380,"style":787},[786],[567,4382],{"className":4383,"style":807},[806],[567,4385],{"className":4386,"style":1174},[1122],[567,4388,1048],{"className":4389},[1178],[567,4391],{"className":4392,"style":1174},[1122],[567,4394,4396,4399],{"className":4395},[601],[567,4397],{"className":4398,"style":2504},[605],[567,4400,2606],{"className":4401},[610],[618,4403,4404],{},"Den Satz für einen Punkt innerhalb des Kreises anwenden. Dort gilt der Sehnensatz.",{"title":4406,"searchDepth":4407,"depth":4407,"links":4408},"",2,[4409,4410,4411,4412],{"id":560,"depth":4407,"text":561},{"id":1671,"depth":4407,"text":1672},{"id":2438,"depth":4407,"text":2439},{"id":3937,"depth":4407,"text":3938},[4414,4416,4418,4421],{"lhs":4415,"rhs":2606},"sqrt(4*9)",{"lhs":4417,"rhs":3207},"sqrt(13^2 - 5^2)",{"lhs":4419,"rhs":4420},"(13 - 5)*(13 + 5)","12^2",{"lhs":4422,"rhs":2534},"36\u002F3 - 3","P \\text{ liegt außerhalb des Kreises}","\u003Cspan class=\"katex\">\u003Cspan class=\"katex-mathml\">\u003Cmath xmlns=\"http:\u002F\u002Fwww.w3.org\u002F1998\u002FMath\u002FMathML\">\u003Csemantics>\u003Cmrow>\u003Cmi>P\u003C\u002Fmi>\u003C\u002Fmrow>\u003Cannotation encoding=\"application\u002Fx-tex\">P\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:0.1389em;\">P\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan> \u003Cspan class=\"katex\">liegt außerhalb des Kreises\u003C\u002Fspan>",null,"md",{"caption":4428,"x":4429,"y":4432,"unit":4435,"items":4436},"Von P aus berührt die Tangente den Kreis in T, die Sekante schneidet ihn in A und 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accent=\"true\">\u003Cmrow>\u003Cmi>P\u003C\u002Fmi>\u003Cmi>A\u003C\u002Fmi>\u003C\u002Fmrow>\u003Cmo stretchy=\"true\">‾\u003C\u002Fmo>\u003C\u002Fmover>\u003Cmo>⋅\u003C\u002Fmo>\u003Cmover accent=\"true\">\u003Cmrow>\u003Cmi>P\u003C\u002Fmi>\u003Cmi>B\u003C\u002Fmi>\u003C\u002Fmrow>\u003Cmo stretchy=\"true\">‾\u003C\u002Fmo>\u003C\u002Fmover>\u003C\u002Fmrow>\u003Cannotation encoding=\"application\u002Fx-tex\">\\overline{PT}^{\\,2} = \\overline{PA} \\cdot \\overline{PB}\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:1.0873em;\">\u003C\u002Fspan>\u003Cspan class=\"mord\">\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\" 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style=\"margin-right:0.1389em;\">P\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>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>","upper",{},true,"\u002Fde\u002Fformulas\u002Fmath\u002Fgeometry\u002Fsekanten-tangenten-satz",[],[4501,4502,4503],"intersecting-chords","pythagorean-theorem","inscribed-angle-theorem",{"title":548,"description":4406},"de\u002Fformulas\u002Fmath\u002Fgeometry\u002Fsekanten-tangenten-satz","Von einem Punkt außerhalb des Kreises ist das Quadrat des Tangentenabschnitts gleich dem Produkt der 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class=\"katex-mathml\">\u003Cmath xmlns=\"http:\u002F\u002Fwww.w3.org\u002F1998\u002FMath\u002FMathML\">\u003Csemantics>\u003Cmrow>\u003Cmi>T\u003C\u002Fmi>\u003C\u002Fmrow>\u003Cannotation encoding=\"application\u002Fx-tex\">T\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:0.1389em;\">T\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>",{"symbol":4521,"meaning":4522,"symbolHtml":4523},"A, B","die beiden Schnittpunkte einer Sekante durch P mit dem Kreis, A liegt näher an P","\u003Cspan class=\"katex\">\u003Cspan class=\"katex-mathml\">\u003Cmath xmlns=\"http:\u002F\u002Fwww.w3.org\u002F1998\u002FMath\u002FMathML\">\u003Csemantics>\u003Cmrow>\u003Cmi>A\u003C\u002Fmi>\u003Cmo separator=\"true\">,\u003C\u002Fmo>\u003Cmi>B\u003C\u002Fmi>\u003C\u002Fmrow>\u003Cannotation encoding=\"application\u002Fx-tex\">A, 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:0.8778em;vertical-align:-0.1944em;\">\u003C\u002Fspan>\u003Cspan class=\"mord mathnormal\">A\u003C\u002Fspan>\u003Cspan class=\"mpunct\">,\u003C\u002Fspan>\u003Cspan class=\"mspace\" style=\"margin-right:0.1667em;\">\u003C\u002Fspan>\u003Cspan class=\"mord mathnormal\" style=\"margin-right:0.0502em;\">B\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>","B8oyCmnykr-sK3a8Goctf6txdkIsdiOIYP5oHIobMfU",[4526,4529,4532],{"stem":4527,"title":4528,"category":247},"de\u002Fformulas\u002Fmath\u002Fgeometry\u002Fsatz-des-pythagoras","Satz des 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