X1411

X80-BETH CONJUGATE OF X80

X1411 = cevapoint of X65 and X1319
< 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, 5 }: Feuerbach Line { 58, 65 }: Central Line L(58, 65) { 56, 244 }: Central Line L(56, 244) { 86, 664 }: Central Line L(86, 664) { 388, 977 }: Central Line L(388, 977) { 269, 1358 }: Central Line L(269, 1358) A = Vertex A (0.0000, 0.0000) B = Vertex B (1.0000, 0.0000) C = Vertex C (0.6122, 0.5999) X_80 = REFLECTION OF INCENTER IN FEUERBACH POINT (0.8980, -0.1000) X_1 = INCENTER (0.5714, 0.2333) X_5 = NINE-POINT CENTER (0.5561, 0.2489) X_58 = ISOGONAL CONJUGATE OF X(10) (0.6107, 0.2850) X_65 = ORTHOCENTER OF THE INTOUCH TRIANGLE (0.6041, 0.2933) X_56 = EXSIMILICENTER(CIRCUMCIRCLE, INCIRCLE) (0.6316, 0.3438) X_244 = -LINE CONJUGATE OF X(100) (0.7857, 0.1166) X_86 = CEVAPOINT OF INCENTER AND CENTROID (0.5534, 0.2171) X_664 = TRILINEAR POLE OF LINE X(2)X(7) (0.2391, 0.5142) X_388 = ∩X(7)X(8) (0.5790, 0.2635) X_977 = ISOGONAL CONJUGATE OF X(976) (0.5890, 0.2525) X_269 = ISOGONAL CONJUGATE OF X(200) (0.6369, 0.3847) X_1358 = BRISSE TRANSFORM OF X(101) (0.7869, 0.1440) X_1411 = -BETH CONJUGATE OF X(80) (1.0110, -0.2153) A B C X80 X1 X5 X58 X65 X56 X244 X86 X664 X388 X977 X269 X1358 X1411 (a, b, c) = (5, 6, 7) | AB = 1

X1411 (X80-BETH CONJUGATE OF X80) constructed on acute reference triangle \((a, b, c) = (5, 6, 7)\) with unit baseline AB = \(1\).

Constructed Elements

Trilinears: \((1 - \cos A)u(a,b,c) : :\), where \(u : v : w\) = X80
Search Value (6, 9, 13): \(-0.804845932982\)
▸ Alternate Coordinates1 form

  • Trilinears: \((1 - \cos A)/(1 - 2 \cos A) : :\)

▸ Incident Central Lines9 lines

{1, 5}, {56, 244}, {58, 65}, {86, 664}, {106, 1168}, {269, 1358}, {388, 977}, {996, 1215}, {1406, 1413}

▸ Functional Relations5 relations