X361

X266-CEVA CONJUGATE OF X1

The isoscelizer equation au(X) = bv(X) = cw(X) has solution X = X361.
< 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, 188 }: Central Line L(1, 188) { 164, 503 }: Central Line L(164, 503) { 266, 978 }: Central Line L(266, 978) A = Vertex A (0.0000, 0.0000) B = Vertex B (1.0000, 0.0000) C = Vertex C (0.6122, 0.5999) X_266 = ISOGONAL CONJUGATE OF X(188) (0.6074, 0.2891) X_1 = INCENTER (0.5714, 0.2333) X_188 = 2nd MID-ARC POINT OF ANTICOMPLEMENTARY TRIANGLE (0.5245, 0.1802) X_164 = INCENTER OF EXCENTRAL TRIANGLE (0.4930, 0.1115) X_503 = 1st ISOSCELIZER POINT (0.5510, 0.1888) X_978 = -CEVA CONJUGATE OF X(1) (0.7456, 0.4040) X_361 = -CEVA CONJUGATE OF X(1) (0.6578, 0.3310) A B C X266 X1 X188 X164 X503 X978 X361 (a, b, c) = (5, 6, 7) | AB = 1

X361 (X266-CEVA CONJUGATE OF X1) constructed on acute reference triangle \((a, b, c) = (5, 6, 7)\) with unit baseline AB = \(1\).

Constructed Elements

Trilinears: \(\csc B/2 + \csc C/2 - \csc A/2 : \csc C/2 + \csc A/2 - \csc B/2 : \csc A/2 + \csc B/2 - \csc C/2\)
Barycentrics: \(f(A,B,C) : f(B,C,A) : f(C,A,B)\), where \(f(A,B,C) = (\sin A)(\csc B/2 + \csc C/2 - \csc A/2)\)
Search Value (6, 9, 13): \(-0.235887433544\)
▸ Incident Central Lines3 lines

{1, 188}, {164, 503}, {266, 978}

▸ Functional Relations1 relation