X1037

CEVAPOINT OF X55 AND X56

X1037 is the cevapoint of X55 and X56.
< 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) { 55, 77 }: Central Line L(55, 77) { 56, 78 }: Central Line L(56, 78) { 29, 388 }: Central Line L(29, 388) { 219, 604 }: Central Line L(219, 604) { 48, 949 }: Central Line L(48, 949) { 73, 1036 }: Central Line L(73, 1036) A = Vertex A (0.0000, 0.0000) B = Vertex B (1.0000, 0.0000) C = Vertex C (0.6122, 0.5999) X_55 = INSIMILICENTER(CIRCUMCIRCLE, INCIRCLE) (0.5490, 0.1921) X_56 = EXSIMILICENTER(CIRCUMCIRCLE, INCIRCLE) (0.6316, 0.3438) X_77 = ISOGONAL CONJUGATE OF X(33) (0.5270, 0.1305) X_78 = ISOGONAL CONJUGATE OF X(34) (0.3835, 0.0491) X_29 = CEVAPOINT OF INCENTER AND ORTHOCENTER (0.5903, 0.3384) X_388 = ∩X(7)X(8) (0.5790, 0.2635) X_219 = -CEVA CONJUGATE OF X(55) (0.4277, 0.0625) X_604 = -CEVA CONJUGATE OF X(31) (0.6442, 0.3744) X_48 = CROSSPOINT OF X(1) AND X(63) (0.5412, 0.1246) X_949 = ISOGONAL CONJUGATE OF X(948) (0.5571, 0.1869) X_73 = CROSSPOINT OF INCENTER AND CIRCUMCENTER (0.5487, 0.1428) X_1036 = ISOGONAL CONJUGATE OF X(388) (0.5632, 0.2044) X_1037 = CEVAPOINT OF X(55) AND X(56) (0.5823, 0.2853) A B C X55 X56 X77 X78 X29 X388 X219 X604 X48 X949 X73 X1036 X1037 (a, b, c) = (5, 6, 7) | AB = 1

X1037 (CEVAPOINT OF X55 AND X56) 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 \(f(A,B,C) = 1/(1 - \cos B \cos C)\)
Barycentrics: \(g(A,B,C) : g(B,C,A) : g(C,A,B)\), where \(g(A,B,C) = (\sin A) f(A,B,C)\)
Search Value (6, 9, 13): \(0.588169280755\)
▸ Incident Central Lines13 lines

{1, 1041}, {3, 1066}, {4, 1067}, {29, 388}, {48, 949}, {55, 77}, {56, 78}, {73, 1036}, {219, 604}, {332, 1014}, {916, 1069}, {1056, 1065}, {1057, 1064}

▸ Functional Relations3 relations