X1272

ISOTOMIC CONJUGATE OF X1138

X1272 is the isotomic conjugate of X1138.
< 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, 1989 }: Central Line L(2, 1989) { 2, 94 }: Central Line L(2, 94) { 69, 74 }: Central Line L(69, 74) 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_1989 = ISOGONAL CONJUGATE OF X(323) (0.9916, -0.2095) X_94 = ISOGONAL CONJUGATE OF X(50) (0.9069, -0.1331) X_69 = SYMMEDIAN POINT OF THE ANTICOMPLEMENTARY TRIANGLE (0.4122, 0.0654) X_74 = ISOGONAL CONJUGATE OF EULER INFINITY POINT (0.7484, -0.3437) X_1272 = ISOTOMIC CONJUGATE OF X(1138) (-0.3710, 1.0188) A B C Ka Kb Kc X2 X1989 X94 X69 X74 X1272 (a, b, c) = (5, 6, 7) | AB = 1

X1272 (ISOTOMIC CONJUGATE OF X1138) constructed on acute reference triangle \((a, b, c) = (5, 6, 7)\) with unit baseline AB = \(1\).

Constructed Elements

Trilinears: \(1/(a^{2}f(a,b,c)) : 1/(b^{2}f(b,c,a)) : 1/(c^{2}f(c,a,b))\), where f(a,b,c) is as in X1138)
Barycentrics: \(a^{8} - 4 a^{6} (b^{2} + c^{2}) + a^{4} (6 b^{4} + b^{2} c^{2} + 6 c^{4}) - a^{2} (4 b^{6} - b^{4} c^{2} - b^{2} c^{4} + 4 c^{6}) + (b^{2} - c^{2})^{2} (b^{4} + 4 b^{2} c^{2} + c^{4}) : :\)
Search Value (6, 9, 13): \(7.995432827522\)
▸ Incident Central Lines2 lines

{2, 94}, {69, 74}

▸ Functional Relations2 relations