X196

X7-CEVA CONJUGATE OF X4

X196 = cevapoint of X19 and X207
< 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) { 4, 65 }: Central Line L(4, 65) { 19, 57 }: Central Line L(19, 57) { 7, 92 }: Central Line L(7, 92) { 55, 108 }: Central Line L(55, 108) { 1, 207 }: Central Line L(1, 207) { 40, 208 }: Central Line L(40, 208) 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_4 = ORTHOCENTER (0.6122, 0.3958) X_65 = ORTHOCENTER OF THE INTOUCH TRIANGLE (0.6041, 0.2933) X_19 = CLAWSON POINT (0.6246, 0.4244) X_57 = ISOGONAL CONJUGATE OF X(9) (0.6138, 0.3110) X_92 = CEVAPOINT OF INCENTER AND CLAWSON POINT (0.5949, 0.3639) X_55 = INSIMILICENTER(CIRCUMCIRCLE, INCIRCLE) (0.5490, 0.1921) X_108 = Ψ(CIRCUMCENTER, INCENTER) (0.5320, 0.6114) X_1 = INCENTER (0.5714, 0.2333) X_207 = -CEVA CONJUGATE OF X(34) (0.5818, 0.9198) X_40 = BEVAN POINT (0.4286, -0.0292) X_208 = -CEVA CONJUGATE OF X(34) (0.6242, -0.2728) X_196 = -CEVA CONJUGATE OF X(4) (0.5649, -0.1989) A B C X7 X4 X65 X19 X57 X92 X55 X108 X1 X207 X40 X208 X196 (a, b, c) = (5, 6, 7) | AB = 1

X196 (X7-CEVA CONJUGATE OF X4) 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 \(f(A,B,C) = (\cos B + \cos C - \cos A - 1) \sec A \tan A/2\)
Barycentrics: \(g(A,B,C) : g(B,C,A) : g(C,A,B)\), where \(g(A,B,C) = (\cos B + \cos C - \cos A - 1) \tan A \tan A/2\)
Search Value (6, 9, 13): \(0.283379483064\)
▸ Incident Central Lines10 lines

{1, 207}, {2, 653}, {4, 65}, {7, 92}, {19, 57}, {34, 937}, {40, 208}, {55, 108}, {226, 281}, {329, 342}

▸ Functional Relations8 relations