X1275

ISOTOMIC CONJUGATE OF X1146

X1275 is the isotomic conjugate of X1146.
< 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) { 7, 59 }: Central Line L(7, 59) { 320, 765 }: Central Line L(320, 765) { 522, 664 }: Central Line L(522, 664) { 651, 666 }: Central Line L(651, 666) { 513, 927 }: Central Line L(513, 927) { 898, 934 }: Central Line L(898, 934) A = Vertex A (0.0000, 0.0000) B = Vertex B (1.0000, 0.0000) C = Vertex C (0.6122, 0.5999) X_1146 = CENTER OF HYPERBOLA {{A,B,C,X(2),X(8)}} (0.6866, 0.0428) X_7 = GERGONNE POINT (0.5903, 0.2769) X_59 = ISOGONAL CONJUGATE OF X(11) (0.5333, 0.4355) X_320 = ISOTOMIC CONJUGATE OF X(80) (-2.6735, -3.5993) X_765 = CEVAPOINT OF X(1) AND X(100) (0.4286, 0.3110) X_522 = ISOGONAL CONJUGATE OF X(109) (-0.0318, 0.3430) X_664 = TRILINEAR POLE OF LINE X(2)X(7) (0.2391, 0.5142) X_651 = TRILINEAR POLE OF LINE X(1)X(3) (0.3048, 0.5599) X_666 = TRILINEAR POLE OF LINE X(2)X(11) (1.0982, 0.1428) X_513 = ISOGONAL CONJUGATE OF X(100) (1.0529, -0.0806) X_927 = ISOGONAL CONJUGATE OF X(926) (1.0037, 0.1836) X_898 = ISOGONAL CONJUGATE OF X(891) (0.9234, -0.1828) X_934 = -CROSS CONJUGATE OF X(57) (0.4269, 0.6071) X_1275 = ISOTOMIC CONJUGATE OF X(1146) (0.5314, 0.4407) A B C X1146 X7 X59 X320 X765 X522 X664 X651 X666 X513 X927 X898 X934 X1275 (a, b, c) = (5, 6, 7) | AB = 1

X1275 (ISOTOMIC CONJUGATE OF X1146) 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 X1146)
Search Value (6, 9, 13): \(0.068228130753\)
▸ Incident Central Lines6 lines

{7, 59}, {320, 765}, {513, 927}, {522, 664}, {651, 666}, {898, 934}

▸ Functional Relations7 relations