X3089

INTERSECTION OF LINES X2X_3 AND X33X_3085

x As a point on the Euler line, X3089 has Shinagawa coefficients \((F, -E)\).
< 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, 3546 }: Euler Line { 2, 3 }: Euler Line { 33, 3085 }: Central Line L(33, 3085) { 34, 3086 }: Central Line L(34, 3086) { 3068, 3092 }: Central Line L(3068, 3092) { 3069, 3093 }: Central Line L(3069, 3093) 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_3546 = EULER LINE INTERCEPT OF LINE X(498)X(1038) (0.4887, 0.0724) X_3 = CIRCUMCENTER (0.5000, 0.1021) X_33 = PERSPECTOR OF THE ORTHIC AND INTANGENTS TRIANGLES (0.6019, 0.3546) X_3085 = INTERSECTION OF LINES X(1)X(2) AND X(4)X(12) (0.5576, 0.2197) X_34 = -BETH CONJUGATE OF X(4) (0.6332, 0.4792) X_3086 = INTERSECTION OF LINES X(1)X(2) AND X(4)X(11) (0.6456, 0.3060) X_3068 = INTERSECTION OF X(2)X(6) AND X(4)X(371) (0.5722, 0.2373) X_3092 = INTERSECTION OF LINES X(2)X(1579) AND X(4)X(6) (0.6095, 0.3668) X_3069 = INTERSECTION OF X(2)X(6) AND X(4)X(372) (0.8529, 0.5391) X_3093 = INTERSECTION OF LINES X(2)X(1578) AND X(4)X(6) (0.6173, 0.4483) X_3089 = INTERSECTION OF LINES X(2)X(3) AND X(33)X(3085) (0.6349, 0.4551) A B C Ka Kb Kc X2 X3546 X3 X33 X3085 X34 X3086 X3068 X3092 X3069 X3093 X3089 (a, b, c) = (5, 6, 7) | AB = 1

X3089 (INTERSECTION OF LINES X2X_3 AND X33X_3085) constructed on acute reference triangle \((a, b, c) = (5, 6, 7)\) with unit baseline AB = \(1\).

Constructed Elements

Trilinears: \(\sec A - \sin B \sin C : :\)
Barycentrics: \(1 - \sec A \csc B \csc C : :\)
Search Value (6, 9, 13): \(-1.422301487713\)
▸ Incident Central Lines5 lines

{2, 3}, {33, 3085}, {34, 3086}, {3068, 3092}, {3069, 3093}

▸ Functional Relations4 relations