X1061

ISOGONAL CONJUGATE OF X1060

X1061 is the isogonal conjugate of X1060.
< 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, 24 }: Central Line L(1, 24) { 33, 80 }: Central Line L(33, 80) { 34, 79 }: Central Line L(34, 79) { 8, 406 }: Central Line L(8, 406) { 21, 1062 }: Central Line L(21, 1062) { 65, 1063 }: Central Line L(65, 1063) A = Vertex A (0.0000, 0.0000) B = Vertex B (1.0000, 0.0000) C = Vertex C (0.6122, 0.5999) X_1060 = INTERSECTION OF LINES X(1)X(3) AND X(5)X(34) (0.5181, 0.1353) X_1 = INCENTER (0.5714, 0.2333) X_24 = PERSPECTOR OF ABC AND ORTHIC-OF-ORTHIC TRIANGLE (0.6627, 0.5278) X_33 = PERSPECTOR OF THE ORTHIC AND INTANGENTS TRIANGLES (0.6019, 0.3546) X_80 = REFLECTION OF INCENTER IN FEUERBACH POINT (0.8980, -0.1000) X_34 = -BETH CONJUGATE OF X(4) (0.6332, 0.4792) X_79 = ISOGONAL CONJUGATE OF X(35) (0.5976, 0.3019) X_8 = NAGEL POINT (0.4694, 0.1333) X_406 = EULER LINE INTERCEPT OF LINE X(10)X(33) (0.5745, 0.2970) X_21 = SCHIFFLER POINT (0.5287, 0.1771) X_1062 = INTERSECTION OF LINES X(1)X(3) AND X(5)X(33) (0.4633, 0.0347) X_65 = ORTHOCENTER OF THE INTOUCH TRIANGLE (0.6041, 0.2933) X_1063 = ISOGONAL CONJUGATE OF X(1062) (0.6152, 0.5187) X_1061 = ISOGONAL CONJUGATE OF X(1060) (0.6067, 0.3472) A B C X1060 X1 X24 X33 X80 X34 X79 X8 X406 X21 X1062 X65 X1063 X1061 (a, b, c) = (5, 6, 7) | AB = 1

X1061 (ISOGONAL CONJUGATE OF X1060) 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 \(f(A,B,C) = 1/(2 + \sec B \sec C)\)
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): \(1.972663630557\)
▸ Incident Central Lines6 lines

{1, 24}, {8, 406}, {21, 1062}, {33, 80}, {34, 79}, {65, 1063}

▸ Functional Relations1 relation