X3187

X27-CEVA CONJUGATE OF X2

X3187 = anticomplement of X306
< 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, 306 }: Nagel Line { 1, 2 }: Nagel Line { 75, 81 }: Central Line L(75, 81) { 31, 740 }: Central Line L(31, 740) { 92, 1172 }: Central Line L(92, 1172) 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_306 = ISOTOMIC CONJUGATE OF X(27) (0.3924, 0.0579) X_1 = INCENTER (0.5714, 0.2333) X_75 = ISOTOMIC CONJUGATE OF INCENTER (0.4988, 0.1682) X_81 = CEVAPOINT OF INCENTER AND SYMMEDIAN POINT (0.5849, 0.2510) X_31 = 2nd POWER POINT (0.6228, 0.3008) X_740 = EVEN (- 1, 1) INFINITY POINT (0.9745, 0.5915) X_92 = CEVAPOINT OF INCENTER AND CLAWSON POINT (0.5949, 0.3639) X_1172 = 1st SARAGOSSA POINT OF X(48) (0.6100, 0.3717) X_3187 = -CEVA CONJUGATE OF X(2) (0.8274, 0.4841) A B C Ka Kb Kc X2 X306 X1 X75 X81 X31 X740 X92 X1172 X3187 (a, b, c) = (5, 6, 7) | AB = 1

X3187 (X27-CEVA CONJUGATE OF X2) 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 \(f(a,b,c) = bc(a^{3} + a^{2}b + a^{2}c - b^{2}c - bc^{2})\) (M. Iliev, 5/13/07)
Barycentrics: \(af(a,b,c) : bf(b,c,a) : cf(c,a,b)\)
Search Value (6, 9, 13): \(-3.931500505128\)
▸ Incident Central Lines10 lines

{1, 2}, {7, 1943}, {31, 740}, {75, 81}, {92, 1172}, {100, 2352}, {193, 1839}, {335, 2606}, {1724, 2901}, {3101, 3164}

▸ Functional Relations5 relations