X504

2nd ISOSCELIZER POINT

The isoscelizer equations [H(A,X)]/a = [H(B,X)]/b = [H(C,X)]/c have solution X = X504. (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) { 164, 173 }: Central Line L(164, 173) A = Vertex A (0.0000, 0.0000) B = Vertex B (1.0000, 0.0000) C = Vertex C (0.6122, 0.5999) X_503 = 1st ISOSCELIZER POINT (0.5510, 0.1888) X_164 = INCENTER OF EXCENTRAL TRIANGLE (0.4930, 0.1115) X_173 = CONGRUENT ISOSCELIZERS POINT (0.5924, 0.2741) X_504 = 2nd ISOSCELIZER POINT (0.4419, 0.0278) A B C X503 X164 X173 X504 (a, b, c) = (5, 6, 7) | AB = 1

X504 (2nd 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 \(f(A,B,C) = b \sin B/2 + c \sin C/2 - a \sin A/2\)
Barycentrics: \(af(A,B,C) : bf(B,C,A) : cf(C,A,B)\)
Search Value (6, 9, 13): \(8.547349049518\)
▸ Incident Central Lines1 line

{164, 173}

▸ Functional Relations3 relations