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r^2",[572,1212,1214,1235,1319,1340,1424],{"className":1213,"ariaHidden":602},[601],[572,1215,1217,1220,1223,1226,1229,1232],{"className":1216},[606],[572,1218],{"className":1219,"style":730},[610],[572,1221,705],{"className":1222},[738],[572,1224,708],{"className":1225},[615,616],[572,1227],{"className":1228,"style":861},[745],[572,1230,793],{"className":1231},[865],[572,1233],{"className":1234,"style":861},[745],[572,1236,1238,1241,1281,1310,1313,1316],{"className":1237},[606],[572,1239],{"className":1240,"style":875},[610],[572,1242,1244,1247],{"className":1243},[615],[572,1245,708],{"className":1246},[615,616],[572,1248,1250],{"className":1249},[885],[572,1251,1253,1273],{"className":1252},[889,890],[572,1254,1256,1270],{"className":1255},[894],[572,1257,1259],{"className":1258,"style":899},[898],[572,1260,1261,1264],{"style":902},[572,1262],{"className":1263,"style":907},[906],[572,1265,1267],{"className":1266},[911,912,913,914],[572,1268,593],{"className":1269,"style":617},[615,616,914],[572,1271,922],{"className":1272},[921],[572,1274,1276],{"className":1275},[894],[572,1277,1279],{"className":1278,"style":929},[898],[572,1280],{},[572,1282,1284,1287],{"className":1283},[767],[572,1285,717],{"className":1286},[767],[572,1288,1290],{"className":1289},[885],[572,1291,1293],{"className":1292},[889],[572,1294,1296],{"className":1295},[894],[572,1297,1299],{"className":1298,"style":950},[898],[572,1300,1301,1304],{"style":953},[572,1302],{"className":1303,"style":907},[906],[572,1305,1307],{"className":1306},[911,912,913,914],[572,1308,809],{"className":1309},[615,914],[572,1311],{"className":1312,"style":861},[745],[572,1314,812],{"className":1315},[865],[572,1317],{"className":1318,"style":861},[745],[572,1320,1322,1325,1328,1331,1334,1337],{"className":1321},[606],[572,1323],{"className":1324,"style":730},[610],[572,1326,705],{"className":1327},[738],[572,1329,714],{"className":1330,"style":763},[615,616],[572,1332],{"className":1333,"style":861},[745],[572,1335,793],{"className":1336},[865],[572,1338],{"className":1339,"style":861},[745],[572,1341,1343,1346,1386,1415,1418,1421],{"className":1342},[606],[572,1344],{"className":1345,"style":875},[610],[572,1347,1349,1352],{"className":1348},[615],[572,1350,714],{"className":1351,"style":763},[615,616],[572,1353,1355],{"className":1354},[885],[572,1356,1358,1378],{"className":1357},[889,890],[572,1359,1361,1375],{"className":1360},[894],[572,1362,1364],{"className":1363,"style":899},[898],[572,1365,1366,1369],{"style":1019},[572,1367],{"className":1368,"style":907},[906],[572,1370,1372],{"className":1371},[911,912,913,914],[572,1373,593],{"className":1374,"style":617},[615,616,914],[572,1376,922],{"className":1377},[921],[572,1379,1381],{"className":1380},[894],[572,1382,1384],{"className":1383,"style":929},[898],[572,1385],{},[572,1387,1389,1392],{"className":1388},[767],[572,1390,717],{"className":1391},[767],[572,1393,1395],{"className":1394},[885],[572,1396,1398],{"className":1397},[889],[572,1399,1401],{"className":1400},[894],[572,1402,1404],{"className":1403,"style":950},[898],[572,1405,1406,1409],{"style":953},[572,1407],{"className":1408,"style":907},[906],[572,1410,1412],{"className":1411},[911,912,913,914],[572,1413,809],{"className":1414},[615,914],[572,1416],{"className":1417,"style":746},[745],[572,1419,1201],{"className":1420},[750],[572,1422],{"className":1423,"style":746},[745],[572,1425,1427,1430],{"className":1426},[606],[572,1428],{"className":1429,"style":950},[610],[572,1431,1433,1436],{"className":1432},[615],[572,1434,633],{"className":1435,"style":649},[615,616],[572,1437,1439],{"className":1438},[885],[572,1440,1442],{"className":1441},[889],[572,1443,1445],{"className":1444},[894],[572,1446,1448],{"className":1447,"style":950},[898],[572,1449,1450,1453],{"style":953},[572,1451],{"className":1452,"style":907},[906],[572,1454,1456],{"className":1455},[911,912,913,914],[572,1457,809],{"className":1458},[615,914],[572,1460,1462,1475],{"className":1461},[575],[572,1463,1465],{"className":1464},[579],[581,1466,1467],{"xmlns":583},[585,1468,1469,1473],{},[588,1470,1471],{},[591,1472,700],{},[595,1474,700],{"encoding":597},[572,1476,1478],{"className":1477,"ariaHidden":602},[601],[572,1479,1481,1484],{"className":1480},[606],[572,1482],{"className":1483,"style":611},[610],[572,1485,700],{"className":1486,"style":734},[615,616],[567,1488,1489],{},"innerhalb",[773,1491,1492,1113,1802,1142,1830,682],{},[572,1493,1495,1554],{"className":1494},[575],[572,1496,1498],{"className":1497},[579],[581,1499,1500],{"xmlns":583},[585,1501,1502,1551],{},[588,1503,1504,1506,1508,1510,1516,1522,1524,1526,1528,1530,1536,1542,1545],{},[702,1505,705],{"stretchy":704},[591,1507,708],{},[702,1509,793],{},[795,1511,1512,1514],{},[591,1513,708],{},[591,1515,593],{},[802,1517,1518,1520],{},[702,1519,717],{"stretchy":704},[807,1521,809],{},[702,1523,812],{},[702,1525,705],{"stretchy":704},[591,1527,714],{},[702,1529,793],{},[795,1531,1532,1534],{},[591,1533,714],{},[591,1535,593],{},[802,1537,1538,1540],{},[702,1539,717],{"stretchy":704},[807,1541,809],{},[702,1543,1544],{},">",[802,1546,1547,1549],{},[591,1548,633],{},[807,1550,809],{},[595,1552,1553],{"encoding":597},"(x - x_M)^2 + (y - y_M)^2 > r^2",[572,1555,1557,1578,1662,1683,1767],{"className":1556,"ariaHidden":602},[601],[572,1558,1560,1563,1566,1569,1572,1575],{"className":1559},[606],[572,1561],{"className":1562,"style":730},[610],[572,1564,705],{"className":1565},[738],[572,1567,708],{"className":1568},[615,616],[572,1570],{"className":1571,"style":861},[745],[572,1573,793],{"className":1574},[865],[572,1576],{"className":1577,"style":861},[745],[572,1579,1581,1584,1624,1653,1656,1659],{"className":1580},[606],[572,1582],{"className":1583,"style":875},[610],[572,1585,1587,1590],{"className":1586},[615],[572,1588,708],{"className":1589},[615,616],[572,1591,1593],{"className":1592},[885],[572,1594,1596,1616],{"className":1595},[889,890],[572,1597,1599,1613],{"className":1598},[894],[572,1600,1602],{"className":1601,"style":899},[898],[572,1603,1604,1607],{"style":902},[572,1605],{"className":1606,"style":907},[906],[572,1608,1610],{"className":1609},[911,912,913,914],[572,1611,593],{"className":1612,"style":617},[615,616,914],[572,1614,922],{"className":1615},[921],[572,1617,1619],{"className":1618},[894],[572,1620,1622],{"className":1621,"style":929},[898],[572,1623],{},[572,1625,1627,1630],{"className":1626},[767],[572,1628,717],{"className":1629},[767],[572,1631,1633],{"className":1632},[885],[572,1634,1636],{"className":1635},[889],[572,1637,1639],{"className":1638},[894],[572,1640,1642],{"className":1641,"style":950},[898],[572,1643,1644,1647],{"style":953},[572,1645],{"className":1646,"style":907},[906],[572,1648,1650],{"className":1649},[911,912,913,914],[572,1651,809],{"className":1652},[615,914],[572,1654],{"className":1655,"style":861},[745],[572,1657,812],{"className":1658},[865],[572,1660],{"className":1661,"style":861},[745],[572,1663,1665,1668,1671,1674,1677,1680],{"className":1664},[606],[572,1666],{"className":1667,"style":730},[610],[572,1669,705],{"className":1670},[738],[572,1672,714],{"className":1673,"style":763},[615,616],[572,1675],{"className":1676,"style":861},[745],[572,1678,793],{"className":1679},[865],[572,1681],{"className":1682,"style":861},[745],[572,1684,1686,1689,1729,1758,1761,1764],{"className":1685},[606],[572,1687],{"className":1688,"style":875},[610],[572,1690,1692,1695],{"className":1691},[615],[572,1693,714],{"className":1694,"style":763},[615,616],[572,1696,1698],{"className":1697},[885],[572,1699,1701,1721],{"className":1700},[889,890],[572,1702,1704,1718],{"className":1703},[894],[572,1705,1707],{"className":1706,"style":899},[898],[572,1708,1709,1712],{"style":1019},[572,1710],{"className":1711,"style":907},[906],[572,1713,1715],{"className":1714},[911,912,913,914],[572,1716,593],{"className":1717,"style":617},[615,616,914],[572,1719,922],{"className":1720},[921],[572,1722,1724],{"className":1723},[894],[572,1725,1727],{"className":1726,"style":929},[898],[572,1728],{},[572,1730,1732,1735],{"className":1731},[767],[572,1733,717],{"className":1734},[767],[572,1736,1738],{"className":1737},[885],[572,1739,1741],{"className":1740},[889],[572,1742,1744],{"className":1743},[894],[572,1745,1747],{"className":1746,"style":950},[898],[572,1748,1749,1752],{"style":953},[572,1750],{"className":1751,"style":907},[906],[572,1753,1755],{"className":1754},[911,912,913,914],[572,1756,809],{"className":1757},[615,914],[572,1759],{"className":1760,"style":746},[745],[572,1762,1544],{"className":1763},[750],[572,1765],{"className":1766,"style":746},[745],[572,1768,1770,1773],{"className":1769},[606],[572,1771],{"className":1772,"style":950},[610],[572,1774,1776,1779],{"className":1775},[615],[572,1777,633],{"className":1778,"style":649},[615,616],[572,1780,1782],{"className":1781},[885],[572,1783,1785],{"className":1784},[889],[572,1786,1788],{"className":1787},[894],[572,1789,1791],{"className":1790,"style":950},[898],[572,1792,1793,1796],{"style":953},[572,1794],{"className":1795,"style":907},[906],[572,1797,1799],{"className":1798},[911,912,913,914],[572,1800,809],{"className":1801},[615,914],[572,1803,1805,1818],{"className":1804},[575],[572,1806,1808],{"className":1807},[579],[581,1809,1810],{"xmlns":583},[585,1811,1812,1816],{},[588,1813,1814],{},[591,1815,700],{},[595,1817,700],{"encoding":597},[572,1819,1821],{"className":1820,"ariaHidden":602},[601],[572,1822,1824,1827],{"className":1823},[606],[572,1825],{"className":1826,"style":611},[610],[572,1828,700],{"className":1829,"style":734},[615,616],[567,1831,1832],{},"außerhalb",[563,1834,1835,1836,682],{},"Liegt der Mittelpunkt im Ursprung, vereinfacht sich die Gleichung zu ",[572,1837,1839,1873],{"className":1838},[575],[572,1840,1842],{"className":1841},[579],[581,1843,1844],{"xmlns":583},[585,1845,1846,1870],{},[588,1847,1848,1854,1856,1862,1864],{},[802,1849,1850,1852],{},[591,1851,708],{},[807,1853,809],{},[702,1855,812],{},[802,1857,1858,1860],{},[591,1859,714],{},[807,1861,809],{},[702,1863,833],{},[802,1865,1866,1868],{},[591,1867,633],{},[807,1869,809],{},[595,1871,1872],{"encoding":597},"x^2 + y^2 = r^2",[572,1874,1876,1921,1966],{"className":1875,"ariaHidden":602},[601],[572,1877,1879,1883,1912,1915,1918],{"className":1878},[606],[572,1880],{"className":1881,"style":1882},[610],"height:0.8974em;vertical-align:-0.0833em;",[572,1884,1886,1889],{"className":1885},[615],[572,1887,708],{"className":1888},[615,616],[572,1890,1892],{"className":1891},[885],[572,1893,1895],{"className":1894},[889],[572,1896,1898],{"className":1897},[894],[572,1899,1901],{"className":1900,"style":950},[898],[572,1902,1903,1906],{"style":953},[572,1904],{"className":1905,"style":907},[906],[572,1907,1909],{"className":1908},[911,912,913,914],[572,1910,809],{"className":1911},[615,914],[572,1913],{"className":1914,"style":861},[745],[572,1916,812],{"className":1917},[865],[572,1919],{"className":1920,"style":861},[745],[572,1922,1924,1928,1957,1960,1963],{"className":1923},[606],[572,1925],{"className":1926,"style":1927},[610],"height:1.0085em;vertical-align:-0.1944em;",[572,1929,1931,1934],{"className":1930},[615],[572,1932,714],{"className":1933,"style":763},[615,616],[572,1935,1937],{"className":1936},[885],[572,1938,1940],{"className":1939},[889],[572,1941,1943],{"className":1942},[894],[572,1944,1946],{"className":1945,"style":950},[898],[572,1947,1948,1951],{"style":953},[572,1949],{"className":1950,"style":907},[906],[572,1952,1954],{"className":1953},[911,912,913,914],[572,1955,809],{"className":1956},[615,914],[572,1958],{"className":1959,"style":746},[745],[572,1961,833],{"className":1962},[750],[572,1964],{"className":1965,"style":746},[745],[572,1967,1969,1972],{"className":1968},[606],[572,1970],{"className":1971,"style":950},[610],[572,1973,1975,1978],{"className":1974},[615],[572,1976,633],{"className":1977,"style":649},[615,616],[572,1979,1981],{"className":1980},[885],[572,1982,1984],{"className":1983},[889],[572,1985,1987],{"className":1986},[894],[572,1988,1990],{"className":1989,"style":950},[898],[572,1991,1992,1995],{"style":953},[572,1993],{"className":1994,"style":907},[906],[572,1996,1998],{"className":1997},[911,912,913,914],[572,1999,809],{"className":2000},[615,914],[563,2002,2003,2004,2007,2008,2225,2226,2254,2255,2284],{},"Multipliziert man aus, erhält man die ",[567,2005,2006],{},"allgemeine Form"," ",[572,2009,2011,2061],{"className":2010},[575],[572,2012,2014],{"className":2013},[579],[581,2015,2016],{"xmlns":583},[585,2017,2018,2058],{},[588,2019,2020,2026,2028,2034,2036,2039,2041,2043,2046,2048,2050,2053,2055],{},[802,2021,2022,2024],{},[591,2023,708],{},[807,2025,809],{},[702,2027,812],{},[802,2029,2030,2032],{},[591,2031,714],{},[807,2033,809],{},[702,2035,812],{},[591,2037,2038],{},"D",[591,2040,708],{},[702,2042,812],{},[591,2044,2045],{},"E",[591,2047,714],{},[702,2049,812],{},[591,2051,2052],{},"F",[702,2054,833],{},[807,2056,2057],{},"0",[595,2059,2060],{"encoding":597},"x^2 + y^2 + Dx + Ey + F = 0",[572,2062,2064,2108,2152,2174,2197,2215],{"className":2063,"ariaHidden":602},[601],[572,2065,2067,2070,2099,2102,2105],{"className":2066},[606],[572,2068],{"className":2069,"style":1882},[610],[572,2071,2073,2076],{"className":2072},[615],[572,2074,708],{"className":2075},[615,616],[572,2077,2079],{"className":2078},[885],[572,2080,2082],{"className":2081},[889],[572,2083,2085],{"className":2084},[894],[572,2086,2088],{"className":2087,"style":950},[898],[572,2089,2090,2093],{"style":953},[572,2091],{"className":2092,"style":907},[906],[572,2094,2096],{"className":2095},[911,912,913,914],[572,2097,809],{"className":2098},[615,914],[572,2100],{"className":2101,"style":861},[745],[572,2103,812],{"className":2104},[865],[572,2106],{"className":2107,"style":861},[745],[572,2109,2111,2114,2143,2146,2149],{"className":2110},[606],[572,2112],{"className":2113,"style":1927},[610],[572,2115,2117,2120],{"className":2116},[615],[572,2118,714],{"className":2119,"style":763},[615,616],[572,2121,2123],{"className":2122},[885],[572,2124,2126],{"className":2125},[889],[572,2127,2129],{"className":2128},[894],[572,2130,2132],{"className":2131,"style":950},[898],[572,2133,2134,2137],{"style":953},[572,2135],{"className":2136,"style":907},[906],[572,2138,2140],{"className":2139},[911,912,913,914],[572,2141,809],{"className":2142},[615,914],[572,2144],{"className":2145,"style":861},[745],[572,2147,812],{"className":2148},[865],[572,2150],{"className":2151,"style":861},[745],[572,2153,2155,2159,2162,2165,2168,2171],{"className":2154},[606],[572,2156],{"className":2157,"style":2158},[610],"height:0.7667em;vertical-align:-0.0833em;",[572,2160,2038],{"className":2161,"style":649},[615,616],[572,2163,708],{"className":2164},[615,616],[572,2166],{"className":2167,"style":861},[745],[572,2169,812],{"className":2170},[865],[572,2172],{"className":2173,"style":861},[745],[572,2175,2177,2181,2185,2188,2191,2194],{"className":2176},[606],[572,2178],{"className":2179,"style":2180},[610],"height:0.8778em;vertical-align:-0.1944em;",[572,2182,2045],{"className":2183,"style":2184},[615,616],"margin-right:0.0576em;",[572,2186,714],{"className":2187,"style":763},[615,616],[572,2189],{"className":2190,"style":861},[745],[572,2192,812],{"className":2193},[865],[572,2195],{"className":2196,"style":861},[745],[572,2198,2200,2203,2206,2209,2212],{"className":2199},[606],[572,2201],{"className":2202,"style":611},[610],[572,2204,2052],{"className":2205,"style":734},[615,616],[572,2207],{"className":2208,"style":746},[745],[572,2210,833],{"className":2211},[750],[572,2213],{"className":2214,"style":746},[745],[572,2216,2218,2222],{"className":2217},[606],[572,2219],{"className":2220,"style":2221},[610],"height:0.6444em;",[572,2223,2057],{"className":2224},[615],". Mittelpunkt und Radius liest man daraus ab, indem man für ",[572,2227,2229,2242],{"className":2228},[575],[572,2230,2232],{"className":2231},[579],[581,2233,2234],{"xmlns":583},[585,2235,2236,2240],{},[588,2237,2238],{},[591,2239,708],{},[595,2241,708],{"encoding":597},[572,2243,2245],{"className":2244,"ariaHidden":602},[601],[572,2246,2248,2251],{"className":2247},[606],[572,2249],{"className":2250,"style":645},[610],[572,2252,708],{"className":2253},[615,616]," und ",[572,2256,2258,2271],{"className":2257},[575],[572,2259,2261],{"className":2260},[579],[581,2262,2263],{"xmlns":583},[585,2264,2265,2269],{},[588,2266,2267],{},[591,2268,714],{},[595,2270,714],{"encoding":597},[572,2272,2274],{"className":2273,"ariaHidden":602},[601],[572,2275,2277,2281],{"className":2276},[606],[572,2278],{"className":2279,"style":2280},[610],"height:0.625em;vertical-align:-0.1944em;",[572,2282,714],{"className":2283,"style":763},[615,616]," jeweils quadratisch ergänzt. Das ergibt nur dann einen Kreis, wenn die rechte Seite danach positiv ist; sonst ist die Lösungsmenge ein einzelner Punkt oder leer.",[558,2286,2288],{"id":2287},"beispiele","Beispiele",[563,2290,2291,2292,2364,2365,2394],{},"Kreis um ",[572,2293,2295,2322],{"className":2294},[575],[572,2296,2298],{"className":2297},[579],[581,2299,2300],{"xmlns":583},[585,2301,2302,2319],{},[588,2303,2304,2306,2308,2310,2312,2314,2317],{},[591,2305,593],{},[702,2307,705],{"stretchy":704},[807,2309,809],{},[702,2311,711],{},[702,2313,793],{},[807,2315,2316],{},"1",[702,2318,717],{"stretchy":704},[595,2320,2321],{"encoding":597},"M(2 \\mid -1)",[572,2323,2325,2349],{"className":2324,"ariaHidden":602},[601],[572,2326,2328,2331,2334,2337,2340,2343,2346],{"className":2327},[606],[572,2329],{"className":2330,"style":730},[610],[572,2332,593],{"className":2333,"style":617},[615,616],[572,2335,705],{"className":2336},[738],[572,2338,809],{"className":2339},[615],[572,2341],{"className":2342,"style":746},[745],[572,2344,711],{"className":2345},[750],[572,2347],{"className":2348,"style":746},[745],[572,2350,2352,2355,2358,2361],{"className":2351},[606],[572,2353],{"className":2354,"style":730},[610],[572,2356,793],{"className":2357},[615],[572,2359,2316],{"className":2360},[615],[572,2362,717],{"className":2363},[767]," mit Radius ",[572,2366,2368,2382],{"className":2367},[575],[572,2369,2371],{"className":2370},[579],[581,2372,2373],{"xmlns":583},[585,2374,2375,2380],{},[588,2376,2377],{},[807,2378,2379],{},"3",[595,2381,2379],{"encoding":597},[572,2383,2385],{"className":2384,"ariaHidden":602},[601],[572,2386,2388,2391],{"className":2387},[606],[572,2389],{"className":2390,"style":2221},[610],[572,2392,2379],{"className":2393},[615],":",[572,2396,2399],{"className":2397},[2398],"katex-display",[572,2400,2402,2450],{"className":2401},[575],[572,2403,2405],{"className":2404},[579],[581,2406,2408],{"xmlns":583,"display":2407},"block",[585,2409,2410,2447],{},[588,2411,2412,2414,2416,2418,2420,2426,2428,2430,2432,2434,2436,2442,2444],{},[702,2413,705],{"stretchy":704},[591,2415,708],{},[702,2417,793],{},[807,2419,809],{},[802,2421,2422,2424],{},[702,2423,717],{"stretchy":704},[807,2425,809],{},[702,2427,812],{},[702,2429,705],{"stretchy":704},[591,2431,714],{},[702,2433,812],{},[807,2435,2316],{},[802,2437,2438,2440],{},[702,2439,717],{"stretchy":704},[807,2441,809],{},[702,2443,833],{},[807,2445,2446],{},"9",[595,2448,2449],{"encoding":597},"(x - 2)^2 + (y + 1)^2 = 9",[572,2451,2453,2474,2524,2545,2592],{"className":2452,"ariaHidden":602},[601],[572,2454,2456,2459,2462,2465,2468,2471],{"className":2455},[606],[572,2457],{"className":2458,"style":730},[610],[572,2460,705],{"className":2461},[738],[572,2463,708],{"className":2464},[615,616],[572,2466],{"className":2467,"style":861},[745],[572,2469,793],{"className":2470},[865],[572,2472],{"className":2473,"style":861},[745],[572,2475,2477,2481,2484,2515,2518,2521],{"className":2476},[606],[572,2478],{"className":2479,"style":2480},[610],"height:1.1141em;vertical-align:-0.25em;",[572,2482,809],{"className":2483},[615],[572,2485,2487,2490],{"className":2486},[767],[572,2488,717],{"className":2489},[767],[572,2491,2493],{"className":2492},[885],[572,2494,2496],{"className":2495},[889],[572,2497,2499],{"className":2498},[894],[572,2500,2503],{"className":2501,"style":2502},[898],"height:0.8641em;",[572,2504,2506,2509],{"style":2505},"top:-3.113em;margin-right:0.05em;",[572,2507],{"className":2508,"style":907},[906],[572,2510,2512],{"className":2511},[911,912,913,914],[572,2513,809],{"className":2514},[615,914],[572,2516],{"className":2517,"style":861},[745],[572,2519,812],{"className":2520},[865],[572,2522],{"className":2523,"style":861},[745],[572,2525,2527,2530,2533,2536,2539,2542],{"className":2526},[606],[572,2528],{"className":2529,"style":730},[610],[572,2531,705],{"className":2532},[738],[572,2534,714],{"className":2535,"style":763},[615,616],[572,2537],{"className":2538,"style":861},[745],[572,2540,812],{"className":2541},[865],[572,2543],{"className":2544,"style":861},[745],[572,2546,2548,2551,2554,2583,2586,2589],{"className":2547},[606],[572,2549],{"className":2550,"style":2480},[610],[572,2552,2316],{"className":2553},[615],[572,2555,2557,2560],{"className":2556},[767],[572,2558,717],{"className":2559},[767],[572,2561,2563],{"className":2562},[885],[572,2564,2566],{"className":2565},[889],[572,2567,2569],{"className":2568},[894],[572,2570,2572],{"className":2571,"style":2502},[898],[572,2573,2574,2577],{"style":2505},[572,2575],{"className":2576,"style":907},[906],[572,2578,2580],{"className":2579},[911,912,913,914],[572,2581,809],{"className":2582},[615,914],[572,2584],{"className":2585,"style":746},[745],[572,2587,833],{"className":2588},[750],[572,2590],{"className":2591,"style":746},[745],[572,2593,2595,2598],{"className":2594},[606],[572,2596],{"className":2597,"style":2221},[610],[572,2599,2446],{"className":2600},[615],[563,2602,2603,2604,2254,2671,2732,2733,2254,2866,2999,3000,3062,3063,682],{},"Die Punkte ",[572,2605,2607,2632],{"className":2606},[575],[572,2608,2610],{"className":2609},[579],[581,2611,2612],{"xmlns":583},[585,2613,2614,2629],{},[588,2615,2616,2618,2621,2623,2625,2627],{},[702,2617,705],{"stretchy":704},[807,2619,2620],{},"5",[702,2622,711],{},[702,2624,793],{},[807,2626,2316],{},[702,2628,717],{"stretchy":704},[595,2630,2631],{"encoding":597},"(5 \\mid -1)",[572,2633,2635,2656],{"className":2634,"ariaHidden":602},[601],[572,2636,2638,2641,2644,2647,2650,2653],{"className":2637},[606],[572,2639],{"className":2640,"style":730},[610],[572,2642,705],{"className":2643},[738],[572,2645,2620],{"className":2646},[615],[572,2648],{"className":2649,"style":746},[745],[572,2651,711],{"className":2652},[750],[572,2654],{"className":2655,"style":746},[745],[572,2657,2659,2662,2665,2668],{"className":2658},[606],[572,2660],{"className":2661,"style":730},[610],[572,2663,793],{"className":2664},[615],[572,2666,2316],{"className":2667},[615],[572,2669,717],{"className":2670},[767],[572,2672,2674,2696],{"className":2673},[575],[572,2675,2677],{"className":2676},[579],[581,2678,2679],{"xmlns":583},[585,2680,2681,2693],{},[588,2682,2683,2685,2687,2689,2691],{},[702,2684,705],{"stretchy":704},[807,2686,809],{},[702,2688,711],{},[807,2690,809],{},[702,2692,717],{"stretchy":704},[595,2694,2695],{"encoding":597},"(2 \\mid 2)",[572,2697,2699,2720],{"className":2698,"ariaHidden":602},[601],[572,2700,2702,2705,2708,2711,2714,2717],{"className":2701},[606],[572,2703],{"className":2704,"style":730},[610],[572,2706,705],{"className":2707},[738],[572,2709,809],{"className":2710},[615],[572,2712],{"className":2713,"style":746},[745],[572,2715,711],{"className":2716},[750],[572,2718],{"className":2719,"style":746},[745],[572,2721,2723,2726,2729],{"className":2722},[606],[572,2724],{"className":2725,"style":730},[610],[572,2727,809],{"className":2728},[615],[572,2730,717],{"className":2731},[767]," liegen darauf: ",[572,2734,2736,2766],{"className":2735},[575],[572,2737,2739],{"className":2738},[579],[581,2740,2741],{"xmlns":583},[585,2742,2743,2763],{},[588,2744,2745,2751,2753,2759,2761],{},[802,2746,2747,2749],{},[807,2748,2379],{},[807,2750,809],{},[702,2752,812],{},[802,2754,2755,2757],{},[807,2756,2057],{},[807,2758,809],{},[702,2760,833],{},[807,2762,2446],{},[595,2764,2765],{"encoding":597},"3^2 + 0^2 = 9",[572,2767,2769,2813,2857],{"className":2768,"ariaHidden":602},[601],[572,2770,2772,2775,2804,2807,2810],{"className":2771},[606],[572,2773],{"className":2774,"style":1882},[610],[572,2776,2778,2781],{"className":2777},[615],[572,2779,2379],{"className":2780},[615],[572,2782,2784],{"className":2783},[885],[572,2785,2787],{"className":2786},[889],[572,2788,2790],{"className":2789},[894],[572,2791,2793],{"className":2792,"style":950},[898],[572,2794,2795,2798],{"style":953},[572,2796],{"className":2797,"style":907},[906],[572,2799,2801],{"className":2800},[911,912,913,914],[572,2802,809],{"className":2803},[615,914],[572,2805],{"className":2806,"style":861},[745],[572,2808,812],{"className":2809},[865],[572,2811],{"className":2812,"style":861},[745],[572,2814,2816,2819,2848,2851,2854],{"className":2815},[606],[572,2817],{"className":2818,"style":950},[610],[572,2820,2822,2825],{"className":2821},[615],[572,2823,2057],{"className":2824},[615],[572,2826,2828],{"className":2827},[885],[572,2829,2831],{"className":2830},[889],[572,2832,2834],{"className":2833},[894],[572,2835,2837],{"className":2836,"style":950},[898],[572,2838,2839,2842],{"style":953},[572,2840],{"className":2841,"style":907},[906],[572,2843,2845],{"className":2844},[911,912,913,914],[572,2846,809],{"className":2847},[615,914],[572,2849],{"className":2850,"style":746},[745],[572,2852,833],{"className":2853},[750],[572,2855],{"className":2856,"style":746},[745],[572,2858,2860,2863],{"className":2859},[606],[572,2861],{"className":2862,"style":2221},[610],[572,2864,2446],{"className":2865},[615],[572,2867,2869,2899],{"className":2868},[575],[572,2870,2872],{"className":2871},[579],[581,2873,2874],{"xmlns":583},[585,2875,2876,2896],{},[588,2877,2878,2884,2886,2892,2894],{},[802,2879,2880,2882],{},[807,2881,2057],{},[807,2883,809],{},[702,2885,812],{},[802,2887,2888,2890],{},[807,2889,2379],{},[807,2891,809],{},[702,2893,833],{},[807,2895,2446],{},[595,2897,2898],{"encoding":597},"0^2 + 3^2 = 9",[572,2900,2902,2946,2990],{"className":2901,"ariaHidden":602},[601],[572,2903,2905,2908,2937,2940,2943],{"className":2904},[606],[572,2906],{"className":2907,"style":1882},[610],[572,2909,2911,2914],{"className":2910},[615],[572,2912,2057],{"className":2913},[615],[572,2915,2917],{"className":2916},[885],[572,2918,2920],{"className":2919},[889],[572,2921,2923],{"className":2922},[894],[572,2924,2926],{"className":2925,"style":950},[898],[572,2927,2928,2931],{"style":953},[572,2929],{"className":2930,"style":907},[906],[572,2932,2934],{"className":2933},[911,912,913,914],[572,2935,809],{"className":2936},[615,914],[572,2938],{"className":2939,"style":861},[745],[572,2941,812],{"className":2942},[865],[572,2944],{"className":2945,"style":861},[745],[572,2947,2949,2952,2981,2984,2987],{"className":2948},[606],[572,2950],{"className":2951,"style":950},[610],[572,2953,2955,2958],{"className":2954},[615],[572,2956,2379],{"className":2957},[615],[572,2959,2961],{"className":2960},[885],[572,2962,2964],{"className":2963},[889],[572,2965,2967],{"className":2966},[894],[572,2968,2970],{"className":2969,"style":950},[898],[572,2971,2972,2975],{"style":953},[572,2973],{"className":2974,"style":907},[906],[572,2976,2978],{"className":2977},[911,912,913,914],[572,2979,809],{"className":2980},[615,914],[572,2982],{"className":2983,"style":746},[745],[572,2985,833],{"className":2986},[750],[572,2988],{"className":2989,"style":746},[745],[572,2991,2993,2996],{"className":2992},[606],[572,2994],{"className":2995,"style":2221},[610],[572,2997,2446],{"className":2998},[615],". Der Punkt ",[572,3001,3003,3026],{"className":3002},[575],[572,3004,3006],{"className":3005},[579],[581,3007,3008],{"xmlns":583},[585,3009,3010,3023],{},[588,3011,3012,3014,3017,3019,3021],{},[702,3013,705],{"stretchy":704},[807,3015,3016],{},"4",[702,3018,711],{},[807,3020,2316],{},[702,3022,717],{"stretchy":704},[595,3024,3025],{"encoding":597},"(4 \\mid 1)",[572,3027,3029,3050],{"className":3028,"ariaHidden":602},[601],[572,3030,3032,3035,3038,3041,3044,3047],{"className":3031},[606],[572,3033],{"className":3034,"style":730},[610],[572,3036,705],{"className":3037},[738],[572,3039,3016],{"className":3040},[615],[572,3042],{"className":3043,"style":746},[745],[572,3045,711],{"className":3046},[750],[572,3048],{"className":3049,"style":746},[745],[572,3051,3053,3056,3059],{"className":3052},[606],[572,3054],{"className":3055,"style":730},[610],[572,3057,2316],{"className":3058},[615],[572,3060,717],{"className":3061},[767]," liegt innerhalb, denn ",[572,3064,3066,3101],{"className":3065},[575],[572,3067,3069],{"className":3068},[579],[581,3070,3071],{"xmlns":583},[585,3072,3073,3098],{},[588,3074,3075,3081,3083,3089,3091,3094,3096],{},[802,3076,3077,3079],{},[807,3078,809],{},[807,3080,809],{},[702,3082,812],{},[802,3084,3085,3087],{},[807,3086,809],{},[807,3088,809],{},[702,3090,833],{},[807,3092,3093],{},"8",[702,3095,1201],{},[807,3097,2446],{},[595,3099,3100],{"encoding":597},"2^2 + 2^2 = 8 \u003C 9",[572,3102,3104,3148,3192,3211],{"className":3103,"ariaHidden":602},[601],[572,3105,3107,3110,3139,3142,3145],{"className":3106},[606],[572,3108],{"className":3109,"style":1882},[610],[572,3111,3113,3116],{"className":3112},[615],[572,3114,809],{"className":3115},[615],[572,3117,3119],{"className":3118},[885],[572,3120,3122],{"className":3121},[889],[572,3123,3125],{"className":3124},[894],[572,3126,3128],{"className":3127,"style":950},[898],[572,3129,3130,3133],{"style":953},[572,3131],{"className":3132,"style":907},[906],[572,3134,3136],{"className":3135},[911,912,913,914],[572,3137,809],{"className":3138},[615,914],[572,3140],{"className":3141,"style":861},[745],[572,3143,812],{"className":3144},[865],[572,3146],{"className":3147,"style":861},[745],[572,3149,3151,3154,3183,3186,3189],{"className":3150},[606],[572,3152],{"className":3153,"style":950},[610],[572,3155,3157,3160],{"className":3156},[615],[572,3158,809],{"className":3159},[615],[572,3161,3163],{"className":3162},[885],[572,3164,3166],{"className":3165},[889],[572,3167,3169],{"className":3168},[894],[572,3170,3172],{"className":3171,"style":950},[898],[572,3173,3174,3177],{"style":953},[572,3175],{"className":3176,"style":907},[906],[572,3178,3180],{"className":3179},[911,912,913,914],[572,3181,809],{"className":3182},[615,914],[572,3184],{"className":3185,"style":746},[745],[572,3187,833],{"className":3188},[750],[572,3190],{"className":3191,"style":746},[745],[572,3193,3195,3199,3202,3205,3208],{"className":3194},[606],[572,3196],{"className":3197,"style":3198},[610],"height:0.6835em;vertical-align:-0.0391em;",[572,3200,3093],{"className":3201},[615],[572,3203],{"className":3204,"style":746},[745],[572,3206,1201],{"className":3207},[750],[572,3209],{"className":3210,"style":746},[745],[572,3212,3214,3217],{"className":3213},[606],[572,3215],{"className":3216,"style":2221},[610],[572,3218,2446],{"className":3219},[615],[563,3221,3222,3223,3436],{},"Mittelpunkt und Radius von ",[572,3224,3226,3274],{"className":3225},[575],[572,3227,3229],{"className":3228},[579],[581,3230,3231],{"xmlns":583},[585,3232,3233,3271],{},[588,3234,3235,3241,3243,3249,3251,3253,3255,3257,3260,3262,3264,3267,3269],{},[802,3236,3237,3239],{},[591,3238,708],{},[807,3240,809],{},[702,3242,812],{},[802,3244,3245,3247],{},[591,3246,714],{},[807,3248,809],{},[702,3250,793],{},[807,3252,3016],{},[591,3254,708],{},[702,3256,812],{},[807,3258,3259],{},"6",[591,3261,714],{},[702,3263,793],{},[807,3265,3266],{},"12",[702,3268,833],{},[807,3270,2057],{},[595,3272,3273],{"encoding":597},"x^2 + y^2 - 4x + 6y - 12 = 0",[572,3275,3277,3321,3365,3387,3409,3427],{"className":3276,"ariaHidden":602},[601],[572,3278,3280,3283,3312,3315,3318],{"className":3279},[606],[572,3281],{"className":3282,"style":1882},[610],[572,3284,3286,3289],{"className":3285},[615],[572,3287,708],{"className":3288},[615,616],[572,3290,3292],{"className":3291},[885],[572,3293,3295],{"className":3294},[889],[572,3296,3298],{"className":3297},[894],[572,3299,3301],{"className":3300,"style":950},[898],[572,3302,3303,3306],{"style":953},[572,3304],{"className":3305,"style":907},[906],[572,3307,3309],{"className":3308},[911,912,913,914],[572,3310,809],{"className":3311},[615,914],[572,3313],{"className":3314,"style":861},[745],[572,3316,812],{"className":3317},[865],[572,3319],{"className":3320,"style":861},[745],[572,3322,3324,3327,3356,3359,3362],{"className":3323},[606],[572,3325],{"className":3326,"style":1927},[610],[572,3328,3330,3333],{"className":3329},[615],[572,3331,714],{"className":3332,"style":763},[615,616],[572,3334,3336],{"className":3335},[885],[572,3337,3339],{"className":3338},[889],[572,3340,3342],{"className":3341},[894],[572,3343,3345],{"className":3344,"style":950},[898],[572,3346,3347,3350],{"style":953},[572,3348],{"className":3349,"style":907},[906],[572,3351,3353],{"className":3352},[911,912,913,914],[572,3354,809],{"className":3355},[615,914],[572,3357],{"className":3358,"style":861},[745],[572,3360,793],{"className":3361},[865],[572,3363],{"className":3364,"style":861},[745],[572,3366,3368,3372,3375,3378,3381,3384],{"className":3367},[606],[572,3369],{"className":3370,"style":3371},[610],"height:0.7278em;vertical-align:-0.0833em;",[572,3373,3016],{"className":3374},[615],[572,3376,708],{"className":3377},[615,616],[572,3379],{"className":3380,"style":861},[745],[572,3382,812],{"className":3383},[865],[572,3385],{"className":3386,"style":861},[745],[572,3388,3390,3394,3397,3400,3403,3406],{"className":3389},[606],[572,3391],{"className":3392,"style":3393},[610],"height:0.8389em;vertical-align:-0.1944em;",[572,3395,3259],{"className":3396},[615],[572,3398,714],{"className":3399,"style":763},[615,616],[572,3401],{"className":3402,"style":861},[745],[572,3404,793],{"className":3405},[865],[572,3407],{"className":3408,"style":861},[745],[572,3410,3412,3415,3418,3421,3424],{"className":3411},[606],[572,3413],{"className":3414,"style":2221},[610],[572,3416,3266],{"className":3417},[615],[572,3419],{"className":3420,"style":746},[745],[572,3422,833],{"className":3423},[750],[572,3425],{"className":3426,"style":746},[745],[572,3428,3430,3433],{"className":3429},[606],[572,3431],{"className":3432,"style":2221},[610],[572,3434,2057],{"className":3435},[615]," durch quadratische Ergänzung:",[572,3438,3440],{"className":3439},[2398],[572,3441,3443,3552],{"className":3442},[575],[572,3444,3446],{"className":3445},[579],[581,3447,3448],{"xmlns":583,"display":2407},[585,3449,3450,3549],{},[588,3451,3452,3454,3460,3462,3464,3466,3468,3470,3472,3474,3476,3482,3484,3486,3488,3490,3492,3494,3496,3498,3500,3502,3504,3506,3509,3512,3514,3516,3518,3520,3522,3528,3530,3532,3534,3536,3538,3544,3546],{},[702,3453,705],{"stretchy":704},[802,3455,3456,3458],{},[591,3457,708],{},[807,3459,809],{},[702,3461,793],{},[807,3463,3016],{},[591,3465,708],{},[702,3467,812],{},[807,3469,3016],{},[702,3471,717],{"stretchy":704},[702,3473,812],{},[702,3475,705],{"stretchy":704},[802,3477,3478,3480],{},[591,3479,714],{},[807,3481,809],{},[702,3483,812],{},[807,3485,3259],{},[591,3487,714],{},[702,3489,812],{},[807,3491,2446],{},[702,3493,717],{"stretchy":704},[702,3495,833],{},[807,3497,3266],{},[702,3499,812],{},[807,3501,3016],{},[702,3503,812],{},[807,3505,2446],{},[745,3507],{"width":3508},"1em",[702,3510,3511],{},"⇒",[745,3513],{"width":3508},[702,3515,705],{"stretchy":704},[591,3517,708],{},[702,3519,793],{},[807,3521,809],{},[802,3523,3524,3526],{},[702,3525,717],{"stretchy":704},[807,3527,809],{},[702,3529,812],{},[702,3531,705],{"stretchy":704},[591,3533,714],{},[702,3535,812],{},[807,3537,2379],{},[802,3539,3540,3542],{},[702,3541,717],{"stretchy":704},[807,3543,809],{},[702,3545,833],{},[807,3547,3548],{},"25",[595,3550,3551],{"encoding":597},"(x^2 - 4x + 4) + (y^2 + 6y + 9) = 12 + 4 + 9\n\\quad\\Rightarrow\\quad\n(x - 2)^2 + (y + 3)^2 = 25",[572,3553,3555,3602,3623,3644,3691,3712,3733,3751,3769,3794,3815,3862,3883,3930],{"className":3554,"ariaHidden":602},[601],[572,3556,3558,3561,3564,3593,3596,3599],{"className":3557},[606],[572,3559],{"className":3560,"style":2480},[610],[572,3562,705],{"className":3563},[738],[572,3565,3567,3570],{"className":3566},[615],[572,3568,708],{"className":3569},[615,616],[572,3571,3573],{"className":3572},[885],[572,3574,3576],{"className":3575},[889],[572,3577,3579],{"className":3578},[894],[572,3580,3582],{"className":3581,"style":2502},[898],[572,3583,3584,3587],{"style":2505},[572,3585],{"className":3586,"style":907},[906],[572,3588,3590],{"className":3589},[911,912,913,914],[572,3591,809],{"className":3592},[615,914],[572,3594],{"className":3595,"style":861},[745],[572,3597,793],{"className":3598},[865],[572,3600],{"className":3601,"style":861},[745],[572,3603,3605,3608,3611,3614,3617,3620],{"className":3604},[606],[572,3606],{"className":3607,"style":3371},[610],[572,3609,3016],{"className":3610},[615],[572,3612,708],{"className":3613},[615,616],[572,3615],{"className":3616,"style":861},[745],[572,3618,812],{"className":3619},[865],[572,3621],{"className":3622,"style":861},[745],[572,3624,3626,3629,3632,3635,3638,3641],{"className":3625},[606],[572,3627],{"className":3628,"style":730},[610],[572,3630,3016],{"className":3631},[615],[572,3633,717],{"className":3634},[767],[572,3636],{"className":3637,"style":861},[745],[572,3639,812],{"className":3640},[865],[572,3642],{"className":3643,"style":861},[745],[572,3645,3647,3650,3653,3682,3685,3688],{"className":3646},[606],[572,3648],{"className":3649,"style":2480},[610],[572,3651,705],{"className":3652},[738],[572,3654,3656,3659],{"className":3655},[615],[572,3657,714],{"className":3658,"style":763},[615,616],[572,3660,3662],{"className":3661},[885],[572,3663,3665],{"className":3664},[889],[572,3666,3668],{"className":3667},[894],[572,3669,3671],{"className":3670,"style":2502},[898],[572,3672,3673,3676],{"style":2505},[572,3674],{"className":3675,"style":907},[906],[572,3677,3679],{"className":3678},[911,912,913,914],[572,3680,809],{"className":3681},[615,914],[572,3683],{"className":3684,"style":861},[745],[572,3686,812],{"className":3687},[865],[572,3689],{"className":3690,"style":861},[745],[572,3692,3694,3697,3700,3703,3706,3709],{"className":3693},[606],[572,3695],{"className":3696,"style":3393},[610],[572,3698,3259],{"className":3699},[615],[572,3701,714],{"className":3702,"style":763},[615,616],[572,3704],{"className":3705,"style":861},[745],[572,3707,812],{"className":3708},[865],[572,3710],{"className":3711,"style":861},[745],[572,3713,3715,3718,3721,3724,3727,3730],{"className":3714},[606],[572,3716],{"className":3717,"style":730},[610],[572,3719,2446],{"className":3720},[615],[572,3722,717],{"className":3723},[767],[572,3725],{"className":3726,"style":746},[745],[572,3728,833],{"className":3729},[750],[572,3731],{"className":3732,"style":746},[745],[572,3734,3736,3739,3742,3745,3748],{"className":3735},[606],[572,3737],{"className":3738,"style":3371},[610],[572,3740,3266],{"className":3741},[615],[572,3743],{"className":3744,"style":861},[745],[572,3746,812],{"className":3747},[865],[572,3749],{"className":3750,"style":861},[745],[572,3752,3754,3757,3760,3763,3766],{"className":3753},[606],[572,3755],{"className":3756,"style":3371},[610],[572,3758,3016],{"className":3759},[615],[572,3761],{"className":3762,"style":861},[745],[572,3764,812],{"className":3765},[865],[572,3767],{"className":3768,"style":861},[745],[572,3770,3772,3775,3778,3782,3785,3788,3791],{"className":3771},[606],[572,3773],{"className":3774,"style":2221},[610],[572,3776,2446],{"className":3777},[615],[572,3779],{"className":3780,"style":3781},[745],"margin-right:1em;",[572,3783],{"className":3784,"style":746},[745],[572,3786,3511],{"className":3787},[750],[572,3789],{"className":3790,"style":3781},[745],[572,3792],{"className":3793,"style":746},[745],[572,3795,3797,3800,3803,3806,3809,3812],{"className":3796},[606],[572,3798],{"className":3799,"style":730},[610],[572,3801,705],{"className":3802},[738],[572,3804,708],{"className":3805},[615,616],[572,3807],{"className":3808,"style":861},[745],[572,3810,793],{"className":3811},[865],[572,3813],{"className":3814,"style":861},[745],[572,3816,3818,3821,3824,3853,3856,3859],{"className":3817},[606],[572,3819],{"className":3820,"style":2480},[610],[572,3822,809],{"className":3823},[615],[572,3825,3827,3830],{"className":3826},[767],[572,3828,717],{"className":3829},[767],[572,3831,3833],{"className":3832},[885],[572,3834,3836],{"className":3835},[889],[572,3837,3839],{"className":3838},[894],[572,3840,3842],{"className":3841,"style":2502},[898],[572,3843,3844,3847],{"style":2505},[572,3845],{"className":3846,"style":907},[906],[572,3848,3850],{"className":3849},[911,912,913,914],[572,3851,809],{"className":3852},[615,914],[572,3854],{"className":3855,"style":861},[745],[572,3857,812],{"className":3858},[865],[572,3860],{"className":3861,"style":861},[745],[572,3863,3865,3868,3871,3874,3877,3880],{"className":3864},[606],[572,3866],{"className":3867,"style":730},[610],[572,3869,705],{"className":3870},[738],[572,3872,714],{"className":3873,"style":763},[615,616],[572,3875],{"className":3876,"style":861},[745],[572,3878,812],{"className":3879},[865],[572,3881],{"className":3882,"style":861},[745],[572,3884,3886,3889,3892,3921,3924,3927],{"className":3885},[606],[572,3887],{"className":3888,"style":2480},[610],[572,3890,2379],{"className":3891},[615],[572,3893,3895,3898],{"className":3894},[767],[572,3896,717],{"className":3897},[767],[572,3899,3901],{"className":3900},[885],[572,3902,3904],{"className":3903},[889],[572,3905,3907],{"className":3906},[894],[572,3908,3910],{"className":3909,"style":2502},[898],[572,3911,3912,3915],{"style":2505},[572,3913],{"className":3914,"style":907},[906],[572,3916,3918],{"className":3917},[911,912,913,914],[572,3919,809],{"className":3920},[615,914],[572,3922],{"className":3923,"style":746},[745],[572,3925,833],{"className":3926},[750],[572,3928],{"className":3929,"style":746},[745],[572,3931,3933,3936],{"className":3932},[606],[572,3934],{"className":3935,"style":2221},[610],[572,3937,3548],{"className":3938},[615],[563,3940,3941,3942,2254,4013,682],{},"Also ",[572,3943,3945,3971],{"className":3944},[575],[572,3946,3948],{"className":3947},[579],[581,3949,3950],{"xmlns":583},[585,3951,3952,3968],{},[588,3953,3954,3956,3958,3960,3962,3964,3966],{},[591,3955,593],{},[702,3957,705],{"stretchy":704},[807,3959,809],{},[702,3961,711],{},[702,3963,793],{},[807,3965,2379],{},[702,3967,717],{"stretchy":704},[595,3969,3970],{"encoding":597},"M(2 \\mid -3)",[572,3972,3974,3998],{"className":3973,"ariaHidden":602},[601],[572,3975,3977,3980,3983,3986,3989,3992,3995],{"className":3976},[606],[572,3978],{"className":3979,"style":730},[610],[572,3981,593],{"className":3982,"style":617},[615,616],[572,3984,705],{"className":3985},[738],[572,3987,809],{"className":3988},[615],[572,3990],{"className":3991,"style":746},[745],[572,3993,711],{"className":3994},[750],[572,3996],{"className":3997,"style":746},[745],[572,3999,4001,4004,4007,4010],{"className":4000},[606],[572,4002],{"className":4003,"style":730},[610],[572,4005,793],{"className":4006},[615],[572,4008,2379],{"className":4009},[615],[572,4011,717],{"className":4012},[767],[572,4014,4016,4034],{"className":4015},[575],[572,4017,4019],{"className":4018},[579],[581,4020,4021],{"xmlns":583},[585,4022,4023,4031],{},[588,4024,4025,4027,4029],{},[591,4026,633],{},[702,4028,833],{},[807,4030,2620],{},[595,4032,4033],{"encoding":597},"r = 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style=\"height:2.7em;\">\u003C\u002Fspan>\u003Cspan class=\"katex-sizing reset-size6 size3 mtight\">\u003Cspan class=\"mord mtight\">2\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"mspace\" style=\"margin-right:0.2778em;\">\u003C\u002Fspan>\u003Cspan class=\"mrel\">=\u003C\u002Fspan>\u003Cspan class=\"mspace\" style=\"margin-right:0.2778em;\">\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"katex-base\">\u003Cspan class=\"katex-strut\" style=\"height:0.8641em;\">\u003C\u002Fspan>\u003Cspan class=\"mord\">\u003Cspan class=\"mord mathnormal\" style=\"margin-right:0.0278em;\">r\u003C\u002Fspan>\u003Cspan class=\"msupsub\">\u003Cspan class=\"vlist-t\">\u003Cspan class=\"vlist-r\">\u003Cspan class=\"vlist\" style=\"height:0.8641em;\">\u003Cspan style=\"top:-3.113em;margin-right:0.05em;\">\u003Cspan class=\"pstrut\" style=\"height:2.7em;\">\u003C\u002Fspan>\u003Cspan class=\"katex-sizing reset-size6 size3 mtight\">\u003Cspan class=\"mord mtight\">2\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>","upper",{},"\u002Fde\u002Fformulas\u002Fmath\u002Fgeometry\u002Fkreisgleichung",[],[4740,4741,4742,4743],"distance-two-points","circle-area","thales-theorem","completing-the-square",{"title":548,"description":4646},"de\u002Fformulas\u002Fmath\u002Fgeometry\u002Fkreisgleichung","Ein Punkt (x | y) liegt genau dann auf dem Kreis um M mit Radius r, wenn sein Abstand zu M gleich r ist.",[4748,4749,4750,4751,4752],"kreis","koordinatensystem","mittelpunkt","radius","analytische geometrie",[4754,4758,4762],{"symbol":4755,"meaning":4756,"symbolHtml":4757},"x, y","Koordinaten eines Punkts auf dem Kreis","\u003Cspan class=\"katex\">\u003Cspan class=\"katex-mathml\">\u003Cmath 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class=\"katex-mathml\">\u003Cmath xmlns=\"http:\u002F\u002Fwww.w3.org\u002F1998\u002FMath\u002FMathML\">\u003Csemantics>\u003Cmrow>\u003Cmsub>\u003Cmi>x\u003C\u002Fmi>\u003Cmi>M\u003C\u002Fmi>\u003C\u002Fmsub>\u003Cmo separator=\"true\">,\u003C\u002Fmo>\u003Cmsub>\u003Cmi>y\u003C\u002Fmi>\u003Cmi>M\u003C\u002Fmi>\u003C\u002Fmsub>\u003C\u002Fmrow>\u003Cannotation encoding=\"application\u002Fx-tex\">x_M, y_M\u003C\u002Fannotation>\u003C\u002Fsemantics>\u003C\u002Fmath>\u003C\u002Fspan>\u003Cspan class=\"katex-html\" aria-hidden=\"true\">\u003Cspan class=\"katex-base\">\u003Cspan class=\"katex-strut\" style=\"height:0.625em;vertical-align:-0.1944em;\">\u003C\u002Fspan>\u003Cspan class=\"mord\">\u003Cspan class=\"mord mathnormal\">x\u003C\u002Fspan>\u003Cspan class=\"msupsub\">\u003Cspan class=\"vlist-t vlist-t2\">\u003Cspan class=\"vlist-r\">\u003Cspan class=\"vlist\" style=\"height:0.3283em;\">\u003Cspan style=\"top:-2.55em;margin-left:0em;margin-right:0.05em;\">\u003Cspan 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