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",[567,1127,1129,1147],{"className":1128},[570],[567,1130,1132],{"className":1131},[574],[576,1133,1134],{"xmlns":578},[580,1135,1136,1144],{},[583,1137,1138,1140,1142],{},[586,1139,588],{},[586,1141,674],{},[586,1143,635],{},[593,1145,1146],{"encoding":595},"ASC",[567,1148,1150],{"className":1149,"ariaHidden":601},[600],[567,1151,1153,1156,1159,1162],{"className":1152},[605],[567,1154],{"className":1155,"style":610},[609],[567,1157,588],{"className":1158},[614,615],[567,1160,674],{"className":1161,"style":689},[614,615],[567,1163,635],{"className":1164,"style":654},[614,615],[567,1166,1168,1186],{"className":1167},[570],[567,1169,1171],{"className":1170},[574],[576,1172,1173],{"xmlns":578},[580,1174,1175,1183],{},[583,1176,1177,1179,1181],{},[586,1178,638],{},[586,1180,674],{},[586,1182,591],{},[593,1184,1185],{"encoding":595},"DSB",[567,1187,1189],{"className":1188,"ariaHidden":601},[600],[567,1190,1192,1195,1198,1201],{"className":1191},[605],[567,1193],{"className":1194,"style":610},[609],[567,1196,638],{"className":1197,"style":658},[614,615],[567,1199,674],{"className":1200,"style":689},[614,615],[567,1202,591],{"className":1203,"style":619},[614,615]," sind ähnlich: Die Winkel bei ",[567,1206,1208,1221],{"className":1207},[570],[567,1209,1211],{"className":1210},[574],[576,1212,1213],{"xmlns":578},[580,1214,1215,1219],{},[583,1216,1217],{},[586,1218,674],{},[593,1220,674],{"encoding":595},[567,1222,1224],{"className":1223,"ariaHidden":601},[600],[567,1225,1227,1230],{"className":1226},[605],[567,1228],{"className":1229,"style":610},[609],[567,1231,674],{"className":1232,"style":689},[614,615]," sind Scheitelwinkel, und die Winkel bei ",[567,1235,1237,1250],{"className":1236},[570],[567,1238,1240],{"className":1239},[574],[576,1241,1242],{"xmlns":578},[580,1243,1244,1248],{},[583,1245,1246],{},[586,1247,588],{},[593,1249,588],{"encoding":595},[567,1251,1253],{"className":1252,"ariaHidden":601},[600],[567,1254,1256,1259],{"className":1255},[605],[567,1257],{"className":1258,"style":610},[609],[567,1260,588],{"className":1261},[614,615],[567,1263,1265,1278],{"className":1264},[570],[567,1266,1268],{"className":1267},[574],[576,1269,1270],{"xmlns":578},[580,1271,1272,1276],{},[583,1273,1274],{},[586,1275,638],{},[593,1277,638],{"encoding":595},[567,1279,1281],{"className":1280,"ariaHidden":601},[600],[567,1282,1284,1287],{"className":1283},[605],[567,1285],{"className":1286,"style":610},[609],[567,1288,638],{"className":1289,"style":658},[614,615]," stehen als Umfangswinkel über demselben Bogen ",[567,1292,1294,1310],{"className":1293},[570],[567,1295,1297],{"className":1296},[574],[576,1298,1299],{"xmlns":578},[580,1300,1301,1307],{},[583,1302,1303,1305],{},[586,1304,591],{},[586,1306,635],{},[593,1308,1309],{"encoding":595},"BC",[567,1311,1313],{"className":1312,"ariaHidden":601},[600],[567,1314,1316,1319,1322],{"className":1315},[605],[567,1317],{"className":1318,"style":610},[609],[567,1320,591],{"className":1321,"style":619},[614,615],[567,1323,635],{"className":1324,"style":654},[614,615],". Aus der Ähnlichkeit folgt",[567,1327,1329],{"className":1328},[850],[567,1330,1332,1445],{"className":1331},[570],[567,1333,1335],{"className":1334},[574],[576,1336,1337],{"xmlns":578,"display":859},[580,1338,1339,1442],{},[583,1340,1341,1364,1366,1388,1391,1394,1396,1406,1408,1418,1420,1430,1432],{},[1342,1343,1344,1354],"mfrac",{},[865,1345,1346,1352],{"accent":601},[583,1347,1348,1350],{},[586,1349,674],{},[586,1351,588],{},[874,1353,876],{"stretchy":601},[865,1355,1356,1362],{"accent":601},[583,1357,1358,1360],{},[586,1359,674],{},[586,1361,638],{},[874,1363,876],{"stretchy":601},[874,1365,892],{},[1342,1367,1368,1378],{},[865,1369,1370,1376],{"accent":601},[583,1371,1372,1374],{},[586,1373,674],{},[586,1375,635],{},[874,1377,876],{"stretchy":601},[865,1379,1380,1386],{"accent":601},[583,1381,1382,1384],{},[586,1383,674],{},[586,1385,591],{},[874,1387,876],{"stretchy":601},[971,1389],{"width":1390},"1em",[874,1392,1393],{},"⇒",[971,1395],{"width":1390},[865,1397,1398,1404],{"accent":601},[583,1399,1400,1402],{},[586,1401,674],{},[586,1403,588],{},[874,1405,876],{"stretchy":601},[874,1407,879],{},[865,1409,1410,1416],{"accent":601},[583,1411,1412,1414],{},[586,1413,674],{},[586,1415,591],{},[874,1417,876],{"stretchy":601},[874,1419,892],{},[865,1421,1422,1428],{"accent":601},[583,1423,1424,1426],{},[586,1425,674],{},[586,1427,635],{},[874,1429,876],{"stretchy":601},[874,1431,879],{},[865,1433,1434,1440],{"accent":601},[583,1435,1436,1438],{},[586,1437,674],{},[586,1439,638],{},[874,1441,876],{"stretchy":601},[593,1443,1444],{"encoding":595},"\\frac{\\overline{SA}}{\\overline{SD}} = \\frac{\\overline{SC}}{\\overline{SB}} \\quad\\Rightarrow\\quad \\overline{SA} \\cdot \\overline{SB} = \\overline{SC} \\cdot \\overline{SD}",[567,1446,1448,1600,1746,1795,1844,1893],{"className":1447,"ariaHidden":601},[600],[567,1449,1451,1455,1591,1594,1597],{"className":1450},[605],[567,1452],{"className":1453,"style":1454},[609],"height:2.3337em;vertical-align:-0.7733em;",[567,1456,1458,1463,1587],{"className":1457},[614],[567,1459],{"className":1460},[1461,1462],"mopen","nulldelimiter",[567,1464,1466],{"className":1465},[1342],[567,1467,1470,1578],{"className":1468},[931,1469],"vlist-t2",[567,1471,1473,1573],{"className":1472},[935],[567,1474,1477,1520,1530],{"className":1475,"style":1476},[939],"height:1.5603em;",[567,1478,1480,1483],{"style":1479},"top:-2.2267em;",[567,1481],{"className":1482,"style":947},[946],[567,1484,1486],{"className":1485},[614],[567,1487,1489],{"className":1488},[614,927],[567,1490,1492],{"className":1491},[931],[567,1493,1495],{"className":1494},[935],[567,1496,1498,1512],{"className":1497,"style":923},[939],[567,1499,1500,1503],{"style":942},[567,1501],{"className":1502,"style":947},[946],[567,1504,1506,1509],{"className":1505},[614],[567,1507,674],{"className":1508,"style":689},[614,615],[567,1510,638],{"className":1511,"style":658},[614,615],[567,1513,1514,1517],{"style":959},[567,1515],{"className":1516,"style":947},[946],[567,1518],{"className":1519,"style":967},[966],[567,1521,1523,1526],{"style":1522},"top:-3.23em;",[567,1524],{"className":1525,"style":947},[946],[567,1527],{"className":1528,"style":967},[1529],"frac-line",[567,1531,1533,1536],{"style":1532},"top:-3.677em;",[567,1534],{"className":1535,"style":947},[946],[567,1537,1539],{"className":1538},[614],[567,1540,1542],{"className":1541},[614,927],[567,1543,1545],{"className":1544},[931],[567,1546,1548],{"className":1547},[935],[567,1549,1551,1565],{"className":1550,"style":923},[939],[567,1552,1553,1556],{"style":942},[567,1554],{"className":1555,"style":947},[946],[567,1557,1559,1562],{"className":1558},[614],[567,1560,674],{"className":1561,"style":689},[614,615],[567,1563,588],{"className":1564},[614,615],[567,1566,1567,1570],{"style":959},[567,1568],{"className":1569,"style":947},[946],[567,1571],{"className":1572,"style":967},[966],[567,1574,1577],{"className":1575},[1576],"vlist-s","​",[567,1579,1581],{"className":1580},[935],[567,1582,1585],{"className":1583,"style":1584},[939],"height:0.7733em;",[567,1586],{},[567,1588],{"className":1589},[1590,1462],"mclose",[567,1592],{"className":1593,"style":1023},[971],[567,1595,892],{"className":1596},[1027],[567,1598],{"className":1599,"style":1023},[971],[567,1601,1603,1606,1730,1734,1737,1740,1743],{"className":1602},[605],[567,1604],{"className":1605,"style":1454},[609],[567,1607,1609,1612,1727],{"className":1608},[614],[567,1610],{"className":1611},[1461,1462],[567,1613,1615],{"className":1614},[1342],[567,1616,1618,1719],{"className":1617},[931,1469],[567,1619,1621,1716],{"className":1620},[935],[567,1622,1624,1666,1674],{"className":1623,"style":1476},[939],[567,1625,1626,1629],{"style":1479},[567,1627],{"className":1628,"style":947},[946],[567,1630,1632],{"className":1631},[614],[567,1633,1635],{"className":1634},[614,927],[567,1636,1638],{"className":1637},[931],[567,1639,1641],{"className":1640},[935],[567,1642,1644,1658],{"className":1643,"style":923},[939],[567,1645,1646,1649],{"style":942},[567,1647],{"className":1648,"style":947},[946],[567,1650,1652,1655],{"className":1651},[614],[567,1653,674],{"className":1654,"style":689},[614,615],[567,1656,591],{"className":1657,"style":619},[614,615],[567,1659,1660,1663],{"style":959},[567,1661],{"className":1662,"style":947},[946],[567,1664],{"className":1665,"style":967},[966],[567,1667,1668,1671],{"style":1522},[567,1669],{"className":1670,"style":947},[946],[567,1672],{"className":1673,"style":967},[1529],[567,1675,1676,1679],{"style":1532},[567,1677],{"className":1678,"style":947},[946],[567,1680,1682],{"className":1681},[614],[567,1683,1685],{"className":1684},[614,927],[567,1686,1688],{"className":1687},[931],[567,1689,1691],{"className":1690},[935],[567,1692,1694,1708],{"className":1693,"style":923},[939],[567,1695,1696,1699],{"style":942},[567,1697],{"className":1698,"style":947},[946],[567,1700,1702,1705],{"className":1701},[614],[567,1703,674],{"className":1704,"style":689},[614,615],[567,1706,635],{"className":1707,"style":654},[614,615],[567,1709,1710,1713],{"style":959},[567,1711],{"className":1712,"style":947},[946],[567,1714],{"className":1715,"style":967},[966],[567,1717,1577],{"className":1718},[1576],[567,1720,1722],{"className":1721},[935],[567,1723,1725],{"className":1724,"style":1584},[939],[567,1726],{},[567,1728],{"className":1729},[1590,1462],[567,1731],{"className":1732,"style":1733},[971],"margin-right:1em;",[567,1735],{"className":1736,"style":1023},[971],[567,1738,1393],{"className":1739},[1027],[567,1741],{"className":1742,"style":1733},[971],[567,1744],{"className":1745,"style":1023},[971],[567,1747,1749,1752,1786,1789,1792],{"className":1748},[605],[567,1750],{"className":1751,"style":923},[609],[567,1753,1755],{"className":1754},[614,927],[567,1756,1758],{"className":1757},[931],[567,1759,1761],{"className":1760},[935],[567,1762,1764,1778],{"className":1763,"style":923},[939],[567,1765,1766,1769],{"style":942},[567,1767],{"className":1768,"style":947},[946],[567,1770,1772,1775],{"className":1771},[614],[567,1773,674],{"className":1774,"style":689},[614,615],[567,1776,588],{"className":1777},[614,615],[567,1779,1780,1783],{"style":959},[567,1781],{"className":1782,"style":947},[946],[567,1784],{"className":1785,"style":967},[966],[567,1787],{"className":1788,"style":972},[971],[567,1790,879],{"className":1791},[976],[567,1793],{"className":1794,"style":972},[971],[567,1796,1798,1801,1835,1838,1841],{"className":1797},[605],[567,1799],{"className":1800,"style":923},[609],[567,1802,1804],{"className":1803},[614,927],[567,1805,1807],{"className":1806},[931],[567,1808,1810],{"className":1809},[935],[567,1811,1813,1827],{"className":1812,"style":923},[939],[567,1814,1815,1818],{"style":942},[567,1816],{"className":1817,"style":947},[946],[567,1819,1821,1824],{"className":1820},[614],[567,1822,674],{"className":1823,"style":689},[614,615],[567,1825,591],{"className":1826,"style":619},[614,615],[567,1828,1829,1832],{"style":959},[567,1830],{"className":1831,"style":947},[946],[567,1833],{"className":1834,"style":967},[966],[567,1836],{"className":1837,"style":1023},[971],[567,1839,892],{"className":1840},[1027],[567,1842],{"className":1843,"style":1023},[971],[567,1845,1847,1850,1884,1887,1890],{"className":1846},[605],[567,1848],{"className":1849,"style":923},[609],[567,1851,1853],{"className":1852},[614,927],[567,1854,1856],{"className":1855},[931],[567,1857,1859],{"className":1858},[935],[567,1860,1862,1876],{"className":1861,"style":923},[939],[567,1863,1864,1867],{"style":942},[567,1865],{"className":1866,"style":947},[946],[567,1868,1870,1873],{"className":1869},[614],[567,1871,674],{"className":1872,"style":689},[614,615],[567,1874,635],{"className":1875,"style":654},[614,615],[567,1877,1878,1881],{"style":959},[567,1879],{"className":1880,"style":947},[946],[567,1882],{"className":1883,"style":967},[966],[567,1885],{"className":1886,"style":972},[971],[567,1888,879],{"className":1889},[976],[567,1891],{"className":1892,"style":972},[971],[567,1894,1896,1899],{"className":1895},[605],[567,1897],{"className":1898,"style":923},[609],[567,1900,1902],{"className":1901},[614,927],[567,1903,1905],{"className":1904},[931],[567,1906,1908],{"className":1907},[935],[567,1909,1911,1925],{"className":1910,"style":923},[939],[567,1912,1913,1916],{"style":942},[567,1914],{"className":1915,"style":947},[946],[567,1917,1919,1922],{"className":1918},[614],[567,1920,674],{"className":1921,"style":689},[614,615],[567,1923,638],{"className":1924,"style":658},[614,615],[567,1926,1927,1930],{"style":959},[567,1928],{"className":1929,"style":947},[946],[567,1931],{"className":1932,"style":967},[966],[558,1934,1936],{"id":1935},"beispiele","Beispiele",[563,1938,1939,1940,1968,1969,620,2018,2061,2062,2090,2091,2134],{},"Eine Sehne wird von ",[567,1941,1943,1956],{"className":1942},[570],[567,1944,1946],{"className":1945},[574],[576,1947,1948],{"xmlns":578},[580,1949,1950,1954],{},[583,1951,1952],{},[586,1953,674],{},[593,1955,674],{"encoding":595},[567,1957,1959],{"className":1958,"ariaHidden":601},[600],[567,1960,1962,1965],{"className":1961},[605],[567,1963],{"className":1964,"style":610},[609],[567,1966,674],{"className":1967,"style":689},[614,615]," in die Abschnitte ",[567,1970,1972,1994],{"className":1971},[570],[567,1973,1975],{"className":1974},[574],[576,1976,1977],{"xmlns":578},[580,1978,1979,1991],{},[583,1980,1981,1984,1988],{},[899,1982,1983],{},"4",[1985,1986,1987],"mtext",{}," ",[1985,1989,1990],{},"cm",[593,1992,1993],{"encoding":595},"4\\,\\text{cm}",[567,1995,1997],{"className":1996,"ariaHidden":601},[600],[567,1998,2000,2004,2007,2011],{"className":1999},[605],[567,2001],{"className":2002,"style":2003},[609],"height:0.6444em;",[567,2005,1983],{"className":2006},[614],[567,2008],{"className":2009,"style":2010},[971],"margin-right:0.1667em;",[567,2012,2015],{"className":2013},[614,2014],"text",[567,2016,1990],{"className":2017},[614],[567,2019,2021,2040],{"className":2020},[570],[567,2022,2024],{"className":2023},[574],[576,2025,2026],{"xmlns":578},[580,2027,2028,2037],{},[583,2029,2030,2033,2035],{},[899,2031,2032],{},"6",[1985,2034,1987],{},[1985,2036,1990],{},[593,2038,2039],{"encoding":595},"6\\,\\text{cm}",[567,2041,2043],{"className":2042,"ariaHidden":601},[600],[567,2044,2046,2049,2052,2055],{"className":2045},[605],[567,2047],{"className":2048,"style":2003},[609],[567,2050,2032],{"className":2051},[614],[567,2053],{"className":2054,"style":2010},[971],[567,2056,2058],{"className":2057},[614,2014],[567,2059,1990],{"className":2060},[614]," geteilt. Eine zweite Sehne durch ",[567,2063,2065,2078],{"className":2064},[570],[567,2066,2068],{"className":2067},[574],[576,2069,2070],{"xmlns":578},[580,2071,2072,2076],{},[583,2073,2074],{},[586,2075,674],{},[593,2077,674],{"encoding":595},[567,2079,2081],{"className":2080,"ariaHidden":601},[600],[567,2082,2084,2087],{"className":2083},[605],[567,2085],{"className":2086,"style":610},[609],[567,2088,674],{"className":2089,"style":689},[614,615]," hat einen Abschnitt von ",[567,2092,2094,2113],{"className":2093},[570],[567,2095,2097],{"className":2096},[574],[576,2098,2099],{"xmlns":578},[580,2100,2101,2110],{},[583,2102,2103,2106,2108],{},[899,2104,2105],{},"3",[1985,2107,1987],{},[1985,2109,1990],{},[593,2111,2112],{"encoding":595},"3\\,\\text{cm}",[567,2114,2116],{"className":2115,"ariaHidden":601},[600],[567,2117,2119,2122,2125,2128],{"className":2118},[605],[567,2120],{"className":2121,"style":2003},[609],[567,2123,2105],{"className":2124},[614],[567,2126],{"className":2127,"style":2010},[971],[567,2129,2131],{"className":2130},[614,2014],[567,2132,1990],{"className":2133},[614],". Der andere ist",[567,2136,2138],{"className":2137},[850],[567,2139,2141,2186],{"className":2140},[570],[567,2142,2144],{"className":2143},[574],[576,2145,2146],{"xmlns":578,"display":859},[580,2147,2148,2183],{},[583,2149,2150,2160,2162,2174,2176,2179,2181],{},[865,2151,2152,2158],{"accent":601},[583,2153,2154,2156],{},[586,2155,674],{},[586,2157,638],{},[874,2159,876],{"stretchy":601},[874,2161,892],{},[1342,2163,2164,2172],{},[583,2165,2166,2168,2170],{},[899,2167,1983],{},[874,2169,879],{},[899,2171,2032],{},[899,2173,2105],{},[874,2175,892],{},[899,2177,2178],{},"8",[1985,2180,1987],{},[1985,2182,1990],{},[593,2184,2185],{"encoding":595},"\\overline{SD} = \\frac{4 \\cdot 6}{3} = 8\\,\\text{cm}",[567,2187,2189,2238,2331],{"className":2188,"ariaHidden":601},[600],[567,2190,2192,2195,2229,2232,2235],{"className":2191},[605],[567,2193],{"className":2194,"style":923},[609],[567,2196,2198],{"className":2197},[614,927],[567,2199,2201],{"className":2200},[931],[567,2202,2204],{"className":2203},[935],[567,2205,2207,2221],{"className":2206,"style":923},[939],[567,2208,2209,2212],{"style":942},[567,2210],{"className":2211,"style":947},[946],[567,2213,2215,2218],{"className":2214},[614],[567,2216,674],{"className":2217,"style":689},[614,615],[567,2219,638],{"className":2220,"style":658},[614,615],[567,2222,2223,2226],{"style":959},[567,2224],{"className":2225,"style":947},[946],[567,2227],{"className":2228,"style":967},[966],[567,2230],{"className":2231,"style":1023},[971],[567,2233,892],{"className":2234},[1027],[567,2236],{"className":2237,"style":1023},[971],[567,2239,2241,2245,2322,2325,2328],{"className":2240},[605],[567,2242],{"className":2243,"style":2244},[609],"height:2.0074em;vertical-align:-0.686em;",[567,2246,2248,2251,2319],{"className":2247},[614],[567,2249],{"className":2250},[1461,1462],[567,2252,2254],{"className":2253},[1342],[567,2255,2257,2310],{"className":2256},[931,1469],[567,2258,2260,2307],{"className":2259},[935],[567,2261,2264,2276,2284],{"className":2262,"style":2263},[939],"height:1.3214em;",[567,2265,2267,2270],{"style":2266},"top:-2.314em;",[567,2268],{"className":2269,"style":947},[946],[567,2271,2273],{"className":2272},[614],[567,2274,2105],{"className":2275},[614],[567,2277,2278,2281],{"style":1522},[567,2279],{"className":2280,"style":947},[946],[567,2282],{"className":2283,"style":967},[1529],[567,2285,2286,2289],{"style":1532},[567,2287],{"className":2288,"style":947},[946],[567,2290,2292,2295,2298,2301,2304],{"className":2291},[614],[567,2293,1983],{"className":2294},[614],[567,2296],{"className":2297,"style":972},[971],[567,2299,879],{"className":2300},[976],[567,2302],{"className":2303,"style":972},[971],[567,2305,2032],{"className":2306},[614],[567,2308,1577],{"className":2309},[1576],[567,2311,2313],{"className":2312},[935],[567,2314,2317],{"className":2315,"style":2316},[939],"height:0.686em;",[567,2318],{},[567,2320],{"className":2321},[1590,1462],[567,2323],{"className":2324,"style":1023},[971],[567,2326,892],{"className":2327},[1027],[567,2329],{"className":2330,"style":1023},[971],[567,2332,2334,2337,2340,2343],{"className":2333},[605],[567,2335],{"className":2336,"style":2003},[609],[567,2338,2178],{"className":2339},[614],[567,2341],{"className":2342,"style":2010},[971],[567,2344,2346],{"className":2345},[614,2014],[567,2347,1990],{"className":2348},[614],[563,2350,2351,2352,2381,2382,2454,2455,2483,2484,2607,2608,846],{},"Kreis mit Radius ",[567,2353,2355,2369],{"className":2354},[570],[567,2356,2358],{"className":2357},[574],[576,2359,2360],{"xmlns":578},[580,2361,2362,2367],{},[583,2363,2364],{},[899,2365,2366],{},"5",[593,2368,2366],{"encoding":595},[567,2370,2372],{"className":2371,"ariaHidden":601},[600],[567,2373,2375,2378],{"className":2374},[605],[567,2376],{"className":2377,"style":2003},[609],[567,2379,2366],{"className":2380},[614]," um den Ursprung, ",[567,2383,2385,2414],{"className":2384},[570],[567,2386,2388],{"className":2387},[574],[576,2389,2390],{"xmlns":578},[580,2391,2392,2411],{},[583,2393,2394,2396,2400,2403,2406,2408],{},[586,2395,674],{},[874,2397,2399],{"stretchy":2398},"false","(",[899,2401,2402],{},"1",[874,2404,2405],{},"∣",[899,2407,901],{},[874,2409,2410],{"stretchy":2398},")",[593,2412,2413],{"encoding":595},"S(1 \\mid 2)",[567,2415,2417,2442],{"className":2416,"ariaHidden":601},[600],[567,2418,2420,2424,2427,2430,2433,2436,2439],{"className":2419},[605],[567,2421],{"className":2422,"style":2423},[609],"height:1em;vertical-align:-0.25em;",[567,2425,674],{"className":2426,"style":689},[614,615],[567,2428,2399],{"className":2429},[1461],[567,2431,2402],{"className":2432},[614],[567,2434],{"className":2435,"style":1023},[971],[567,2437,2405],{"className":2438},[1027],[567,2440],{"className":2441,"style":1023},[971],[567,2443,2445,2448,2451],{"className":2444},[605],[567,2446],{"className":2447,"style":2423},[609],[567,2449,901],{"className":2450},[614],[567,2452,2410],{"className":2453},[1590],". Die waagerechte Sehne durch ",[567,2456,2458,2471],{"className":2457},[570],[567,2459,2461],{"className":2460},[574],[576,2462,2463],{"xmlns":578},[580,2464,2465,2469],{},[583,2466,2467],{},[586,2468,674],{},[593,2470,674],{"encoding":595},[567,2472,2474],{"className":2473,"ariaHidden":601},[600],[567,2475,2477,2480],{"className":2476},[605],[567,2478],{"className":2479,"style":610},[609],[567,2481,674],{"className":2482,"style":689},[614,615]," hat die Enden ",[567,2485,2487,2513],{"className":2486},[570],[567,2488,2490],{"className":2489},[574],[576,2491,2492],{"xmlns":578},[580,2493,2494,2510],{},[583,2495,2496,2499,2501,2504],{},[586,2497,2498],{},"x",[874,2500,892],{},[874,2502,2503],{},"±",[2505,2506,2507],"msqrt",{},[899,2508,2509],{},"21",[593,2511,2512],{"encoding":595},"x = \\pm\\sqrt{21}",[567,2514,2516,2534],{"className":2515,"ariaHidden":601},[600],[567,2517,2519,2522,2525,2528,2531],{"className":2518},[605],[567,2520],{"className":2521,"style":813},[609],[567,2523,2498],{"className":2524},[614,615],[567,2526],{"className":2527,"style":1023},[971],[567,2529,892],{"className":2530},[1027],[567,2532],{"className":2533,"style":1023},[971],[567,2535,2537,2541,2544],{"className":2536},[605],[567,2538],{"className":2539,"style":2540},[609],"height:1.04em;vertical-align:-0.1328em;",[567,2542,2503],{"className":2543},[614],[567,2545,2548],{"className":2546},[614,2547],"sqrt",[567,2549,2551,2598],{"className":2550},[931,1469],[567,2552,2554,2595],{"className":2553},[935],[567,2555,2558,2572],{"className":2556,"style":2557},[939],"height:0.9072em;",[567,2559,2562,2565],{"className":2560,"style":942},[2561],"svg-align",[567,2563],{"className":2564,"style":947},[946],[567,2566,2569],{"className":2567,"style":2568},[614],"padding-left:0.833em;",[567,2570,2509],{"className":2571},[614],[567,2573,2575,2578],{"style":2574},"top:-2.8672em;",[567,2576],{"className":2577,"style":947},[946],[567,2579,2583],{"className":2580,"style":2582},[2581],"hide-tail","min-width:0.853em;height:1.08em;",[2584,2585,2591],"svg",{"xmlns":2586,"width":2587,"height":2588,"viewBox":2589,"preserveAspectRatio":2590},"http:\u002F\u002Fwww.w3.org\u002F2000\u002Fsvg","400em","1.08em","0 0 400000 1080","xMinYMin slice",[2592,2593],"path",{"d":2594},"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",[567,2596,1577],{"className":2597},[1576],[567,2599,2601],{"className":2600},[935],[567,2602,2605],{"className":2603,"style":2604},[939],"height:0.1328em;",[567,2606],{},", die senkrechte die Enden ",[567,2609,2611,2635],{"className":2610},[570],[567,2612,2614],{"className":2613},[574],[576,2615,2616],{"xmlns":578},[580,2617,2618,2632],{},[583,2619,2620,2623,2625,2627],{},[586,2621,2622],{},"y",[874,2624,892],{},[874,2626,2503],{},[2505,2628,2629],{},[899,2630,2631],{},"24",[593,2633,2634],{"encoding":595},"y = \\pm\\sqrt{24}",[567,2636,2638,2658],{"className":2637,"ariaHidden":601},[600],[567,2639,2641,2645,2649,2652,2655],{"className":2640},[605],[567,2642],{"className":2643,"style":2644},[609],"height:0.625em;vertical-align:-0.1944em;",[567,2646,2622],{"className":2647,"style":2648},[614,615],"margin-right:0.0359em;",[567,2650],{"className":2651,"style":1023},[971],[567,2653,892],{"className":2654},[1027],[567,2656],{"className":2657,"style":1023},[971],[567,2659,2661,2664,2667],{"className":2660},[605],[567,2662],{"className":2663,"style":2540},[609],[567,2665,2503],{"className":2666},[614],[567,2668,2670],{"className":2669},[614,2547],[567,2671,2673,2706],{"className":2672},[931,1469],[567,2674,2676,2703],{"className":2675},[935],[567,2677,2679,2691],{"className":2678,"style":2557},[939],[567,2680,2682,2685],{"className":2681,"style":942},[2561],[567,2683],{"className":2684,"style":947},[946],[567,2686,2688],{"className":2687,"style":2568},[614],[567,2689,2631],{"className":2690},[614],[567,2692,2693,2696],{"style":2574},[567,2694],{"className":2695,"style":947},[946],[567,2697,2699],{"className":2698,"style":2582},[2581],[2584,2700,2701],{"xmlns":2586,"width":2587,"height":2588,"viewBox":2589,"preserveAspectRatio":2590},[2592,2702],{"d":2594},[567,2704,1577],{"className":2705},[1576],[567,2707,2709],{"className":2708},[935],[567,2710,2712],{"className":2711,"style":2604},[939],[567,2713],{},[567,2715,2717],{"className":2716},[850],[567,2718,2720,2796],{"className":2719},[570],[567,2721,2723],{"className":2722},[574],[576,2724,2725],{"xmlns":578,"display":859},[580,2726,2727,2793],{},[583,2728,2729,2743,2758,2760,2763,2765,2779],{},[583,2730,2731,2733,2737,2739,2741],{},[874,2732,2399],{"fence":601},[2505,2734,2735],{},[899,2736,2509],{},[874,2738,904],{},[899,2740,2402],{},[874,2742,2410],{"fence":601},[583,2744,2745,2747,2751,2754,2756],{},[874,2746,2399],{"fence":601},[2505,2748,2749],{},[899,2750,2509],{},[874,2752,2753],{},"+",[899,2755,2402],{},[874,2757,2410],{"fence":601},[874,2759,892],{},[899,2761,2762],{},"20",[874,2764,892],{},[583,2766,2767,2769,2773,2775,2777],{},[874,2768,2399],{"fence":601},[2505,2770,2771],{},[899,2772,2631],{},[874,2774,904],{},[899,2776,901],{},[874,2778,2410],{"fence":601},[583,2780,2781,2783,2787,2789,2791],{},[874,2782,2399],{"fence":601},[2505,2784,2785],{},[899,2786,2631],{},[874,2788,2753],{},[899,2790,901],{},[874,2792,2410],{"fence":601},[593,2794,2795],{"encoding":595},"\\left(\\sqrt{21} - 1\\right)\\left(\\sqrt{21} + 1\\right) = 20 = \\left(\\sqrt{24} - 2\\right)\\left(\\sqrt{24} + 2\\right)",[567,2797,2799,2974,2992],{"className":2798,"ariaHidden":601},[600],[567,2800,2802,2806,2888,2891,2965,2968,2971],{"className":2801},[605],[567,2803],{"className":2804,"style":2805},[609],"height:1.8em;vertical-align:-0.65em;",[567,2807,2810,2820,2870,2873,2876,2879,2882],{"className":2808},[2809],"minner",[567,2811,2815],{"className":2812,"style":2814},[1461,2813],"delimcenter","top:0em;",[567,2816,2399],{"className":2817},[2818,2819],"delimsizing","size2",[567,2821,2823],{"className":2822},[614,2547],[567,2824,2826,2861],{"className":2825},[931,1469],[567,2827,2829,2858],{"className":2828},[935],[567,2830,2833,2845],{"className":2831,"style":2832},[939],"height:0.9561em;",[567,2834,2836,2839],{"className":2835,"style":942},[2561],[567,2837],{"className":2838,"style":947},[946],[567,2840,2842],{"className":2841,"style":2568},[614],[567,2843,2509],{"className":2844},[614],[567,2846,2848,2851],{"style":2847},"top:-2.9161em;",[567,2849],{"className":2850,"style":947},[946],[567,2852,2854],{"className":2853,"style":2582},[2581],[2584,2855,2856],{"xmlns":2586,"width":2587,"height":2588,"viewBox":2589,"preserveAspectRatio":2590},[2592,2857],{"d":2594},[567,2859,1577],{"className":2860},[1576],[567,2862,2864],{"className":2863},[935],[567,2865,2868],{"className":2866,"style":2867},[939],"height:0.0839em;",[567,2869],{},[567,2871],{"className":2872,"style":972},[971],[567,2874,904],{"className":2875},[976],[567,2877],{"className":2878,"style":972},[971],[567,2880,2402],{"className":2881},[614],[567,2883,2885],{"className":2884,"style":2814},[1590,2813],[567,2886,2410],{"className":2887},[2818,2819],[567,2889],{"className":2890,"style":2010},[971],[567,2892,2894,2900,2947,2950,2953,2956,2959],{"className":2893},[2809],[567,2895,2897],{"className":2896,"style":2814},[1461,2813],[567,2898,2399],{"className":2899},[2818,2819],[567,2901,2903],{"className":2902},[614,2547],[567,2904,2906,2939],{"className":2905},[931,1469],[567,2907,2909,2936],{"className":2908},[935],[567,2910,2912,2924],{"className":2911,"style":2832},[939],[567,2913,2915,2918],{"className":2914,"style":942},[2561],[567,2916],{"className":2917,"style":947},[946],[567,2919,2921],{"className":2920,"style":2568},[614],[567,2922,2509],{"className":2923},[614],[567,2925,2926,2929],{"style":2847},[567,2927],{"className":2928,"style":947},[946],[567,2930,2932],{"className":2931,"style":2582},[2581],[2584,2933,2934],{"xmlns":2586,"width":2587,"height":2588,"viewBox":2589,"preserveAspectRatio":2590},[2592,2935],{"d":2594},[567,2937,1577],{"className":2938},[1576],[567,2940,2942],{"className":2941},[935],[567,2943,2945],{"className":2944,"style":2867},[939],[567,2946],{},[567,2948],{"className":2949,"style":972},[971],[567,2951,2753],{"className":2952},[976],[567,2954],{"className":2955,"style":972},[971],[567,2957,2402],{"className":2958},[614],[567,2960,2962],{"className":2961,"style":2814},[1590,2813],[567,2963,2410],{"className":2964},[2818,2819],[567,2966],{"className":2967,"style":1023},[971],[567,2969,892],{"className":2970},[1027],[567,2972],{"className":2973,"style":1023},[971],[567,2975,2977,2980,2983,2986,2989],{"className":2976},[605],[567,2978],{"className":2979,"style":2003},[609],[567,2981,2762],{"className":2982},[614],[567,2984],{"className":2985,"style":1023},[971],[567,2987,892],{"className":2988},[1027],[567,2990],{"className":2991,"style":1023},[971],[567,2993,2995,2998,3072,3075],{"className":2994},[605],[567,2996],{"className":2997,"style":2805},[609],[567,2999,3001,3007,3054,3057,3060,3063,3066],{"className":3000},[2809],[567,3002,3004],{"className":3003,"style":2814},[1461,2813],[567,3005,2399],{"className":3006},[2818,2819],[567,3008,3010],{"className":3009},[614,2547],[567,3011,3013,3046],{"className":3012},[931,1469],[567,3014,3016,3043],{"className":3015},[935],[567,3017,3019,3031],{"className":3018,"style":2832},[939],[567,3020,3022,3025],{"className":3021,"style":942},[2561],[567,3023],{"className":3024,"style":947},[946],[567,3026,3028],{"className":3027,"style":2568},[614],[567,3029,2631],{"className":3030},[614],[567,3032,3033,3036],{"style":2847},[567,3034],{"className":3035,"style":947},[946],[567,3037,3039],{"className":3038,"style":2582},[2581],[2584,3040,3041],{"xmlns":2586,"width":2587,"height":2588,"viewBox":2589,"preserveAspectRatio":2590},[2592,3042],{"d":2594},[567,3044,1577],{"className":3045},[1576],[567,3047,3049],{"className":3048},[935],[567,3050,3052],{"className":3051,"style":2867},[939],[567,3053],{},[567,3055],{"className":3056,"style":972},[971],[567,3058,904],{"className":3059},[976],[567,3061],{"className":3062,"style":972},[971],[567,3064,901],{"className":3065},[614],[567,3067,3069],{"className":3068,"style":2814},[1590,2813],[567,3070,2410],{"className":3071},[2818,2819],[567,3073],{"className":3074,"style":2010},[971],[567,3076,3078,3084,3131,3134,3137,3140,3143],{"className":3077},[2809],[567,3079,3081],{"className":3080,"style":2814},[1461,2813],[567,3082,2399],{"className":3083},[2818,2819],[567,3085,3087],{"className":3086},[614,2547],[567,3088,3090,3123],{"className":3089},[931,1469],[567,3091,3093,3120],{"className":3092},[935],[567,3094,3096,3108],{"className":3095,"style":2832},[939],[567,3097,3099,3102],{"className":3098,"style":942},[2561],[567,3100],{"className":3101,"style":947},[946],[567,3103,3105],{"className":3104,"style":2568},[614],[567,3106,2631],{"className":3107},[614],[567,3109,3110,3113],{"style":2847},[567,3111],{"className":3112,"style":947},[946],[567,3114,3116],{"className":3115,"style":2582},[2581],[2584,3117,3118],{"xmlns":2586,"width":2587,"height":2588,"viewBox":2589,"preserveAspectRatio":2590},[2592,3119],{"d":2594},[567,3121,1577],{"className":3122},[1576],[567,3124,3126],{"className":3125},[935],[567,3127,3129],{"className":3128,"style":2867},[939],[567,3130],{},[567,3132],{"className":3133,"style":972},[971],[567,3135,2753],{"className":3136},[976],[567,3138],{"className":3139,"style":972},[971],[567,3141,901],{"className":3142},[614],[567,3144,3146],{"className":3145,"style":2814},[1590,2813],[567,3147,2410],{"className":3148},[2818,2819],[563,3150,3151,3152,3334],{},"Das stimmt mit ",[567,3153,3155,3194],{"className":3154},[570],[567,3156,3158],{"className":3157},[574],[576,3159,3160],{"xmlns":578},[580,3161,3162,3191],{},[583,3163,3164,3170,3172,3178,3180,3183,3185,3187,3189],{},[894,3165,3166,3168],{},[586,3167,801],{},[899,3169,901],{},[874,3171,904],{},[894,3173,3174,3176],{},[586,3175,770],{},[899,3177,901],{},[874,3179,892],{},[899,3181,3182],{},"25",[874,3184,904],{},[899,3186,2366],{},[874,3188,892],{},[899,3190,2762],{},[593,3192,3193],{"encoding":595},"r^2 - d^2 = 25 - 5 = 20",[567,3195,3197,3244,3288,3307,3325],{"className":3196,"ariaHidden":601},[600],[567,3198,3200,3204,3235,3238,3241],{"className":3199},[605],[567,3201],{"className":3202,"style":3203},[609],"height:0.8974em;vertical-align:-0.0833em;",[567,3205,3207,3210],{"className":3206},[614],[567,3208,801],{"className":3209,"style":658},[614,615],[567,3211,3213],{"className":3212},[1047],[567,3214,3216],{"className":3215},[931],[567,3217,3219],{"className":3218},[935],[567,3220,3223],{"className":3221,"style":3222},[939],"height:0.8141em;",[567,3224,3226,3229],{"style":3225},"top:-3.063em;margin-right:0.05em;",[567,3227],{"className":3228,"style":1064},[946],[567,3230,3232],{"className":3231},[1068,1069,1070,1071],[567,3233,901],{"className":3234},[614,1071],[567,3236],{"className":3237,"style":972},[971],[567,3239,904],{"className":3240},[976],[567,3242],{"className":3243,"style":972},[971],[567,3245,3247,3250,3279,3282,3285],{"className":3246},[605],[567,3248],{"className":3249,"style":3222},[609],[567,3251,3253,3256],{"className":3252},[614],[567,3254,770],{"className":3255},[614,615],[567,3257,3259],{"className":3258},[1047],[567,3260,3262],{"className":3261},[931],[567,3263,3265],{"className":3264},[935],[567,3266,3268],{"className":3267,"style":3222},[939],[567,3269,3270,3273],{"style":3225},[567,3271],{"className":3272,"style":1064},[946],[567,3274,3276],{"className":3275},[1068,1069,1070,1071],[567,3277,901],{"className":3278},[614,1071],[567,3280],{"className":3281,"style":1023},[971],[567,3283,892],{"className":3284},[1027],[567,3286],{"className":3287,"style":1023},[971],[567,3289,3291,3295,3298,3301,3304],{"className":3290},[605],[567,3292],{"className":3293,"style":3294},[609],"height:0.7278em;vertical-align:-0.0833em;",[567,3296,3182],{"className":3297},[614],[567,3299],{"className":3300,"style":972},[971],[567,3302,904],{"className":3303},[976],[567,3305],{"className":3306,"style":972},[971],[567,3308,3310,3313,3316,3319,3322],{"className":3309},[605],[567,3311],{"className":3312,"style":2003},[609],[567,3314,2366],{"className":3315},[614],[567,3317],{"className":3318,"style":1023},[971],[567,3320,892],{"className":3321},[1027],[567,3323],{"className":3324,"style":1023},[971],[567,3326,3328,3331],{"className":3327},[605],[567,3329],{"className":3330,"style":2003},[609],[567,3332,2762],{"className":3333},[614]," überein.",[558,3336,3338],{"id":3337},"typische-fehler","Typische Fehler",[3340,3341,3342,3480,3483],"ul",{},[3343,3344,3345,3346,3475,3476,3479],"li",{},"Die Abschnitte über Kreuz multiplizieren, also ",[567,3347,3349,3383],{"className":3348},[570],[567,3350,3352],{"className":3351},[574],[576,3353,3354],{"xmlns":578},[580,3355,3356,3380],{},[583,3357,3358,3368,3370],{},[865,3359,3360,3366],{"accent":601},[583,3361,3362,3364],{},[586,3363,674],{},[586,3365,588],{},[874,3367,876],{"stretchy":601},[874,3369,879],{},[865,3371,3372,3378],{"accent":601},[583,3373,3374,3376],{},[586,3375,674],{},[586,3377,635],{},[874,3379,876],{"stretchy":601},[593,3381,3382],{"encoding":595},"\\overline{SA} \\cdot \\overline{SC}",[567,3384,3386,3435],{"className":3385,"ariaHidden":601},[600],[567,3387,3389,3392,3426,3429,3432],{"className":3388},[605],[567,3390],{"className":3391,"style":923},[609],[567,3393,3395],{"className":3394},[614,927],[567,3396,3398],{"className":3397},[931],[567,3399,3401],{"className":3400},[935],[567,3402,3404,3418],{"className":3403,"style":923},[939],[567,3405,3406,3409],{"style":942},[567,3407],{"className":3408,"style":947},[946],[567,3410,3412,3415],{"className":3411},[614],[567,3413,674],{"className":3414,"style":689},[614,615],[567,3416,588],{"className":3417},[614,615],[567,3419,3420,3423],{"style":959},[567,3421],{"className":3422,"style":947},[946],[567,3424],{"className":3425,"style":967},[966],[567,3427],{"className":3428,"style":972},[971],[567,3430,879],{"className":3431},[976],[567,3433],{"className":3434,"style":972},[971],[567,3436,3438,3441],{"className":3437},[605],[567,3439],{"className":3440,"style":923},[609],[567,3442,3444],{"className":3443},[614,927],[567,3445,3447],{"className":3446},[931],[567,3448,3450],{"className":3449},[935],[567,3451,3453,3467],{"className":3452,"style":923},[939],[567,3454,3455,3458],{"style":942},[567,3456],{"className":3457,"style":947},[946],[567,3459,3461,3464],{"className":3460},[614],[567,3462,674],{"className":3463,"style":689},[614,615],[567,3465,635],{"className":3466,"style":654},[614,615],[567,3468,3469,3472],{"style":959},[567,3470],{"className":3471,"style":947},[946],[567,3473],{"className":3474,"style":967},[966],". Multipliziert werden die beiden Teile ",[692,3477,3478],{},"derselben"," Sehne.",[3343,3481,3482],{},"Ganze Sehnenlängen statt Abschnitte einsetzen.",[3343,3484,3485],{},"Den Satz anwenden, wenn sich die Geraden außerhalb des Kreises schneiden. Dann gilt der Sekantensatz.",{"title":3487,"searchDepth":3488,"depth":3488,"links":3489},"",2,[3490,3491,3492,3493],{"id":560,"depth":3488,"text":561},{"id":1121,"depth":3488,"text":1122},{"id":1935,"depth":3488,"text":1936},{"id":3337,"depth":3488,"text":3338},[3495,3497,3499,3501],{"lhs":3496,"rhs":2178},"4*6\u002F3",{"lhs":3498,"rhs":2762},"(sqrt(21) - 1)*(sqrt(21) + 1)",{"lhs":3500,"rhs":2762},"(sqrt(24) - 2)*(sqrt(24) + 2)",{"lhs":3502,"rhs":2762},"5^2 - (1^2 + 2^2)","S \\text{ liegt im Inneren des Kreises}","\u003Cspan class=\"katex\">\u003Cspan class=\"katex-mathml\">\u003Cmath xmlns=\"http:\u002F\u002Fwww.w3.org\u002F1998\u002FMath\u002FMathML\">\u003Csemantics>\u003Cmrow>\u003Cmi>S\u003C\u002Fmi>\u003C\u002Fmrow>\u003Cannotation encoding=\"application\u002Fx-tex\">S\u003C\u002Fannotation>\u003C\u002Fsemantics>\u003C\u002Fmath>\u003C\u002Fspan>\u003Cspan class=\"katex-html\" aria-hidden=\"true\">\u003Cspan class=\"katex-base\">\u003Cspan class=\"katex-strut\" 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style=\"height:3em;\">\u003C\u002Fspan>\u003Cspan class=\"mord\">\u003Cspan class=\"mord mathnormal\" style=\"margin-right:0.0576em;\">S\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>",{"symbol":3592,"meaning":3593,"symbolHtml":3594},"\\overline{SC}, \\overline{SD}","Längen der beiden Abschnitte der zweiten Sehne CD","\u003Cspan class=\"katex\">\u003Cspan class=\"katex-mathml\">\u003Cmath xmlns=\"http:\u002F\u002Fwww.w3.org\u002F1998\u002FMath\u002FMathML\">\u003Csemantics>\u003Cmrow>\u003Cmover 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