X1369

ANTICOMPLEMENTARY CONJUGATE OF X6

X1369 = anticomplement of X251
< A B C >: Reference Triangle △ABC < K_a K_b K_c >: Anticomplementary Triangle △K_a K_b K_c [ A B ]: Sideline AB (Base c = 1) [ B C ]: Sideline BC (Side a) [ C A ]: Sideline CA (Side b) { 2, 251 }: Central Line L(2, 251) { 2, 32 }: Central Line L(2, 32) { 69, 3410 }: Central Line L(69, 3410) A = Vertex A (0.0000, 0.0000) B = Vertex B (1.0000, 0.0000) C = Vertex C (0.6122, 0.5999) K_a = Anticomplementary Vertex K_a (1.6122, 0.5999) K_b = Anticomplementary Vertex K_b (-0.3878, 0.5999) K_c = Anticomplementary Vertex K_c (0.3878, -0.5999) X_2 = CENTROID (0.5374, 0.2000) X_251 = ISOGONAL CONJUGATE OF X(141) (0.6177, 0.3042) X_32 = 3rd POWER POINT (0.6400, 0.3332) X_69 = SYMMEDIAN POINT OF THE ANTICOMPLEMENTARY TRIANGLE (0.4122, 0.0654) X_3410 = INTERSECTION OF LINES X(2)X(98) AND X(4)X(93) (0.4988, 0.2469) X_1369 = ANTICOMPLEMENTARY CONJUGATE OF X(6) (0.3769, -0.0086) A B C Ka Kb Kc X2 X251 X32 X69 X3410 X1369 (a, b, c) = (5, 6, 7) | AB = 1

X1369 (ANTICOMPLEMENTARY CONJUGATE OF X6) constructed on acute reference triangle \((a, b, c) = (5, 6, 7)\) with unit baseline AB = \(1\).

Constructed Elements

Trilinears: \(f(a,b,c) : f(b,c,a) : f(c,a,b)\), where \(f(a,b,c) = bc[b^{2}/(a^{2} + c^{2}) + c^{2}/(a^{2} + b^{2}) - a^{2}/(b^{2} + c^{2})]\)
Barycentrics: \(g(a,b,c) : g(b,c,a) : g(c,a,b)\), where \(g(a,b,c) = b^{2}/(a^{2} + c^{2}) + c^{2}/(a^{2} + b^{2}) - a^{2}/(b^{2} + c^{2})\)
Search Value (6, 9, 13): \(6.742808371976\)
▸ Incident Central Lines2 lines

{2, 32}, {69, 3410}

▸ Functional Relations5 relations