X503

1st ISOSCELIZER POINT

The isoscelizer equations aH(A,X) = bH(B,X) = cH(C,X) have solution X = X503. (Peter Yff, 4/9/99)
< 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) { 1, 167 }: Central Line L(1, 167) { 164, 361 }: Central Line L(164, 361) { 173, 844 }: Central Line L(173, 844) A = Vertex A (0.0000, 0.0000) B = Vertex B (1.0000, 0.0000) C = Vertex C (0.6122, 0.5999) X_259 = ISOGONAL CONJUGATE OF X(174) (0.5606, 0.2123) X_1 = INCENTER (0.5714, 0.2333) X_167 = NAGEL POINT OF EXCENTRAL TRIANGLE (0.4425, -0.0480) X_164 = INCENTER OF EXCENTRAL TRIANGLE (0.4930, 0.1115) X_361 = -CEVA CONJUGATE OF X(1) (0.6578, 0.3310) X_173 = CONGRUENT ISOSCELIZERS POINT (0.5924, 0.2741) X_844 = INTERSECTION OF LINES X(166)X(167) AND X(173)X(503) (0.4606, 0.0024) X_503 = 1st ISOSCELIZER POINT (0.5510, 0.1888) A B C X259 X1 X167 X164 X361 X173 X844 X503 (a, b, c) = (5, 6, 7) | AB = 1

X503 (1st ISOSCELIZER POINT) 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 \(f(A,B,C) = \sec B/2 + \sec C/2 - \sec A/2\)
Barycentrics: \(af(A,B,C) : bf(B,C,A) : cf(C,A,B)\)
Search Value (6, 9, 13): \(3.065720157040\)
▸ Incident Central Lines3 lines

{1, 167}, {164, 361}, {173, 844}

▸ Functional Relations4 relations