X3263

ISOTOMIC CONJUGATE OF X105

X3263 is the isotomic conjugate of X105.
< 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, 3290 }: Central Line L(2, 3290) { 2, 37 }: Central Line L(2, 37) { 8, 304 }: Central Line L(8, 304) { 85, 341 }: Central Line L(85, 341) { 325, 523 }: Central Line L(325, 523) 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_3290 = INTERSECTION OF LINES X(2)X(37) AND X(230)X(231) (1.0664, 0.6348) X_37 = CROSSPOINT OF INCENTER AND CENTROID (0.5567, 0.2158) X_8 = NAGEL POINT (0.4694, 0.1333) X_304 = ISOTOMIC CONJUGATE OF X(19) (0.3683, 0.0513) X_85 = ISOTOMIC CONJUGATE OF X(9) (0.5610, 0.2421) X_341 = ISOTOMIC CONJUGATE OF X(269) (0.3509, 0.0650) X_325 = -HIRST INVERSE OF X(69) (-0.3370, -0.7398) X_523 = ISOGONAL CONJUGATE OF X(110) (1.0856, -0.0096) X_3263 = ISOTOMIC CONJUGATE OF X(105) (-0.5206, -0.6696) A B C Ka Kb Kc X2 X3290 X37 X8 X304 X85 X341 X325 X523 X3263 (a, b, c) = (5, 6, 7) | AB = 1

X3263 (ISOTOMIC CONJUGATE OF X105) 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 \(f(a,b,c) = (b^{2} + c^{2} - ab - ac)/a^{2}\)
Barycentrics: \(af(a,b,c) : bf(b,c,a) : cf(c,a,b)\)
Search Value (6, 9, 13): \(8.892960693067\)
▸ Incident Central Lines15 lines

{2, 37}, {8, 304}, {10, 1930}, {85, 341}, {99, 1325}, {100, 2862}, {104, 2865}, {109, 2866}, {274, 1390}, {305, 561}, {313, 1233}, {314, 2346}, {325, 523}, {442, 1228}, {742, 2238}

▸ Functional Relations9 relations