X1065

ISOGONAL CONJUGATE OF X1064

X1065 is the isogonal conjugate of X1064.
< 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) { 102, 226 }: Central Line L(102, 226) { 3, 388 }: Central Line L(3, 388) { 284, 515 }: Central Line L(284, 515) { 4, 1036 }: Central Line L(4, 1036) { 283, 1010 }: Central Line L(283, 1010) { 497, 1057 }: Central Line L(497, 1057) A = Vertex A (0.0000, 0.0000) B = Vertex B (1.0000, 0.0000) C = Vertex C (0.6122, 0.5999) X_1064 = INTERSECTION OF LINES X(1)X(4) AND X(3)X(31) (0.5648, 0.2070) X_102 = Λ(INCENTER, ORTHOCENTER) (0.6364, -0.3897) X_226 = -CEVA CONJUGATE OF X(65) (0.5778, 0.2588) X_3 = CIRCUMCENTER (0.5000, 0.1021) X_388 = ∩X(7)X(8) (0.5790, 0.2635) X_284 = -CROSS CONJUGATE OF X(21) (0.5646, 0.2088) X_515 = ISOGONAL CONJUGATE OF X(102) (0.6804, 0.7691) X_4 = ORTHOCENTER (0.6122, 0.3958) X_1036 = ISOGONAL CONJUGATE OF X(388) (0.5632, 0.2044) X_283 = -CROSS CONJUGATE OF X(21) (0.4475, 0.0704) X_1010 = INTERCEPT OF EULER LINE AND LINE X(1)X(75) (0.5391, 0.2043) X_497 = CROSSPOINT OF GERGONNE POINT AND NAGEL POINT (0.5593, 0.1851) X_1057 = ISOGONAL CONJUGATE OF X(1056) (0.5671, 0.2170) X_1065 = ISOGONAL CONJUGATE OF X(1064) (0.5777, 0.2607) A B C X1064 X102 X226 X3 X388 X284 X515 X4 X1036 X283 X1010 X497 X1057 X1065 (a, b, c) = (5, 6, 7) | AB = 1

X1065 (ISOGONAL CONJUGATE OF X1064) 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 \(f(A,B,C) = 1/[1 + \cos A (\cos B + \cos C)]\)
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): \(0.433671240986\)
▸ Incident Central Lines7 lines

{3, 388}, {4, 1036}, {102, 226}, {283, 1010}, {284, 515}, {497, 1057}, {1037, 1056}

▸ Functional Relations2 relations