X2223

X2-ISOCONJUGATE OF X673

X2223 = X92-isoconjugate of X1814
< A B C >: Reference Triangle △ABC [ A B ]: Sideline AB (Base c = 1) [ B C ]: Sideline BC (Side a) [ C A ]: Sideline CA (Side b) { 1, 3 }: OI Line (Incenter–Circumcenter Line) { 31, 32 }: Central Line L(31, 32) { 39, 42 }: Central Line L(39, 42) { 100, 239 }: Central Line L(100, 239) { 187, 237 }: Central Line L(187, 237) { 10, 1009 }: Central Line L(10, 1009) A = Vertex A (0.0000, 0.0000) B = Vertex B (1.0000, 0.0000) C = Vertex C (0.6122, 0.5999) X_2481 = INTERSECTION(FEUERBACH HYPERBOLA, STEINER CIRCUMELLIPSE) (0.9225, -0.0635) X_1 = INCENTER (0.5714, 0.2333) X_3 = CIRCUMCENTER (0.5000, 0.1021) X_31 = 2nd POWER POINT (0.6228, 0.3008) X_32 = 3rd POWER POINT (0.6400, 0.3332) X_39 = BROCARD MIDPOINT (0.5778, 0.2305) X_42 = CROSSPOINT OF INCENTER AND SYMMEDIAN POINT (0.5880, 0.2495) X_100 = ANTICOMPLEMENT OF FEUERBACH POINT (0.1429, 0.4666) X_239 = -LINE CONJUGATE OF X(42) (4.2109, 3.7992) X_187 = INVERSE-IN-CIRCUMCIRCLE OF X(6) (SCHOUTE CENTER) (1.1986, 1.2559) X_237 = -LINE CONJUGATE OF X(2) (0.9894, 1.3825) X_10 = SPIEKER CENTER (0.5204, 0.1833) X_1009 = INTERCEPT OF EULER LINE AND LINE X(1)X(39) (0.5532, 0.2412) X_2223 = -ISOCONJUGATE OF X(673) (1.1455, 1.2880) A B C X2481 X1 X3 X31 X32 X39 X42 X100 X239 X187 X237 X10 X1009 X2223 (a, b, c) = (5, 6, 7) | AB = 1

X2223 (X2-ISOCONJUGATE OF X673) constructed on acute reference triangle \((a, b, c) = (5, 6, 7)\) with unit baseline AB = \(1\).

Constructed Elements

Trilinears: \(a/f(a,b,c) : b/f(b,c,a) : c/f(c,a,b)\), where f(a,b,c) is as in X673
Search Value (6, 9, 13): \(-1.660324838543\)
▸ Alternate Coordinates1 form

  • Trilinears: \(a^{2}(as - S_{\omega }) : b^{2}(bs - S_{\omega }) : c^{2}(cs - S_{\omega }) (César Lozada, 9/07/2013)\)

▸ Incident Central Lines26 lines

{1, 3}, {6, 2279}, {10, 1009}, {31, 32}, {39, 42}, {48, 2175}, {100, 239}, {187, 237}, {212, 1397}, {238, 2110}, {292, 1438}, {516, 1284}, {572, 2330}, {574, 2177}, {604, 1253}, {612, 2340}, {674, 2245}, {760, 1959}, {991, 1469}, {1014, 2346}, {1037, 1804}, {1110, 2149}, {1400, 2293}, {1423, 1742}, {1486, 2178}, {1918, 1964}

▸ Functional Relations8 relations