X3100

INTERSECTION OF LINES X1X_7 AND X2X_33

X3100 = anticomplement of X1861
< 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, 1861 }: Central Line L(2, 1861) { 1, 7 }: Soddy Line { 2, 33 }: Central Line L(2, 33) { 22, 55 }: Central Line L(22, 55) { 21, 270 }: Central Line L(21, 270) 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_1861 = ZOSMA TRANSFORM OF X(238) (0.8061, 0.8443) X_1 = INCENTER (0.5714, 0.2333) X_7 = GERGONNE POINT (0.5903, 0.2769) X_33 = PERSPECTOR OF THE ORTHIC AND INTANGENTS TRIANGLES (0.6019, 0.3546) X_22 = EXETER POINT (0.4143, -0.1221) X_55 = INSIMILICENTER(CIRCUMCIRCLE, INCIRCLE) (0.5490, 0.1921) X_21 = SCHIFFLER POINT (0.5287, 0.1771) X_270 = ISOGONAL CONJUGATE OF X(201) (0.6168, 0.3881) X_3100 = INTERSECTION OF LINES X(1)X(7) AND X(2)X(33) (0.0000, -1.0887) A B C Ka Kb Kc X2 X1861 X1 X7 X33 X22 X55 X21 X270 X3100 (a, b, c) = (5, 6, 7) | AB = 1

X3100 (INTERSECTION OF LINES X1X_7 AND X2X_33) 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 \(f(a,b,c) = (b + c - a)(b^{4} + c^{4} - a^{4} - bc(b^{2} + c^{2} - a^{2}))\)
Barycentrics: \(af(a,b,c) : bf(b,c,a) : cf(c,a,b)\)
Search Value (6, 9, 13): \(4.147544654784\)
▸ Incident Central Lines21 lines

{1, 7}, {2, 33}, {4, 1062}, {11, 858}, {21, 270}, {22, 55}, {30, 1870}, {36, 2071}, {78, 280}, {165, 3100}, {229, 2646}, {238, 2310}, {376, 1060}, {394, 2192}, {497, 1370}, {518, 677}, {522, 663}, {651, 971}, {655, 1807}, {984, 1253}, {1776, 2361}

▸ Functional Relations3 relations