X234

X7-CEVA CONJUGATE OF X177

X234 = X7-Ceva conjugate of X177
< 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) { 2, 178 }: Central Line L(2, 178) { 7, 174 }: Central Line L(7, 174) { 57, 362 }: Central Line L(57, 362) { 75, 556 }: Central Line L(75, 556) { 555, 1088 }: Central Line L(555, 1088) A = Vertex A (0.0000, 0.0000) B = Vertex B (1.0000, 0.0000) C = Vertex C (0.6122, 0.5999) X_7 = GERGONNE POINT (0.5903, 0.2769) X_177 = 1st MID-ARC POINT (0.5862, 0.2654) X_2 = CENTROID (0.5374, 0.2000) X_178 = 2nd MID-ARC POINT (0.5439, 0.2098) X_174 = YFF CENTER OF CONGRUENCE (0.5813, 0.2549) X_57 = ISOGONAL CONJUGATE OF X(9) (0.6138, 0.3110) X_362 = CONGRUENT CIRCUMCIRCLES ISOSCELIZER POINT (0.5299, 0.2081) X_75 = ISOTOMIC CONJUGATE OF INCENTER (0.4988, 0.1682) X_556 = (X(1),X(75))-ANSWER TO QUESTION A (0.4842, 0.1501) X_555 = (X(1),X(158))-ANSWER TO QUESTION A (0.5982, 0.2990) X_1088 = TRILINEAR SQUARE OF X(7) (0.6052, 0.3210) X_234 = -CEVA CONJUGATE OF X(177) (0.5946, 0.2875) A B C X7 X177 X2 X178 X174 X57 X362 X75 X556 X555 X1088 X234 (a, b, c) = (5, 6, 7) | AB = 1

X234 (X7-CEVA CONJUGATE OF X177) 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 \(f(A,B,C) = (\cos B/2 + \cos C/2)(\cos B/2 \cos C/2)^{2}\)
Barycentrics: \((\sin A)f(A,B,C) : (\sin B)f(B,C,A) : (\sin C)f(C,A,B)\)
Search Value (6, 9, 13): \(0.597068718087\)
▸ Incident Central Lines5 lines

{2, 178}, {7, 174}, {57, 362}, {75, 556}, {555, 1088}

▸ Functional Relations2 relations