X844

INTERSECTION OF LINES X166X_167 AND X173X_503

X844 = X75-of-excentral-triangle
< 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) { 166, 167 }: Central Line L(166, 167) { 173, 503 }: Central Line L(173, 503) A = Vertex A (0.0000, 0.0000) B = Vertex B (1.0000, 0.0000) C = Vertex C (0.6122, 0.5999) X_164 = INCENTER OF EXCENTRAL TRIANGLE (0.4930, 0.1115) X_166 = GERGONNE POINT OF EXCENTRAL TRIANGLE (0.5156, 0.1554) X_167 = NAGEL POINT OF EXCENTRAL TRIANGLE (0.4425, -0.0480) X_173 = CONGRUENT ISOSCELIZERS POINT (0.5924, 0.2741) X_503 = 1st ISOSCELIZER POINT (0.5510, 0.1888) X_844 = INTERSECTION OF LINES X(166)X(167) AND X(173)X(503) (0.4606, 0.0024) A B C X164 X166 X167 X173 X503 X844 (a, b, c) = (5, 6, 7) | AB = 1

X844 (INTERSECTION OF LINES X166X_167 AND X173X_503) constructed on acute reference triangle \((a, b, c) = (5, 6, 7)\) with unit baseline AB = \(1\).

Constructed Elements

Trilinears: \(- x + y + z : :\), where \(x = x(A,B,C) = \sin(A/2) \sec^{2}(A/2)\)
Search Value (6, 9, 13): \(11.987336626371\)
▸ Incident Central Lines2 lines

{166, 167}, {173, 503}

▸ Functional Relations2 relations

Notes

This point solves a problem posed by Antreas Hatzipolakis in Hyacinthos #2768, May 3, 2001.