X3763

X3618com[T(a², a² + c²)]

< 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) { 2, 6 }: Centroid–Symmedian Line { 66, 154 }: Central Line L(66, 154) { 49, 182 }: Central Line L(49, 182) { 5, 1350 }: Central Line L(5, 1350) { 140, 1352 }: Central Line L(140, 1352) { 159, 1853 }: Central Line L(159, 1853) A = Vertex A (0.0000, 0.0000) B = Vertex B (1.0000, 0.0000) C = Vertex C (0.6122, 0.5999) X_2 = CENTROID (0.5374, 0.2000) X_6 = SYMMEDIAN POINT (LEMOINE POINT, GREBE POINT) (0.6000, 0.2672) X_66 = ISOGONAL CONJUGATE OF X(22) (0.5912, 1.0593) X_154 = -CEVA CONJUGATE OF X(6) (0.4807, -0.3954) X_49 = CENTER OF SINE-TRIPLE-ANGLE CIRCLE (0.6275, 0.1789) X_182 = MIDPOINT OF BROCARD DIAMETER (0.5500, 0.1846) X_5 = NINE-POINT CENTER (0.5561, 0.2489) X_1350 = REFLECTION OF X(6) IN X(3) (0.4000, -0.0631) X_140 = MIDPOINT OF X(3) AND X(5) (0.5281, 0.1755) X_1352 = REFLECTION OF X(6) IN X(5) (0.5122, 0.2306) X_159 = -OF-TANGENTIAL-TRIANGLE (0.4211, -0.7266) X_1853 = ZOSMA TRANSFORM OF X(204) (0.5941, 0.7953) X_3763 = com[T(a2, a2 + c2)] (0.5249, 0.1865) A B C X2 X6 X66 X154 X49 X182 X5 X1350 X140 X1352 X159 X1853 X3763 (a, b, c) = (5, 6, 7) | AB = 1

X3763 (X3618com[T(a², a² + c²)]) constructed on acute reference triangle \((a, b, c) = (5, 6, 7)\) with unit baseline AB = \(1\).

Constructed Elements

Barycentrics: \(a^{2} + 2b^{2} + 2c^{2} : b^{2} + 2c^{2} + 2a^{2} : c^{2} + 2a^{2} + 2b^{2}\)
Search Value (6, 9, 13): \(2.956660851973\)
▸ Incident Central Lines19 lines

{2, 6}, {3, 2916}, {5, 1350}, {10, 3242}, {49, 182}, {66, 154}, {125, 2930}, {140, 1352}, {159, 1853}, {316, 2076}, {381, 3098}, {511, 1656}, {518, 1698}, {631, 1503}, {632, 3564}, {1086, 2345}, {1125, 3416}, {1386, 3624}, {2097, 3452}