X1021

ISOGONAL CONJUGATE OF X1020

X1021 is the isogonal conjugate of X1020.
< 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, 647 }: Central Line L(1, 647) { 239, 514 }: Central Line L(239, 514) { 243, 522 }: Central Line L(243, 522) { 521, 650 }: Central Line L(521, 650) { 648, 1020 }: Central Line L(648, 1020) { 333, 1024 }: Central Line L(333, 1024) A = Vertex A (0.0000, 0.0000) B = Vertex B (1.0000, 0.0000) C = Vertex C (0.6122, 0.5999) X_81 = CEVAPOINT OF INCENTER AND SYMMEDIAN POINT (0.5849, 0.2510) X_162 = CEVAPOINT OF X(108) AND X(109) (0.4897, 0.6018) X_1 = INCENTER (0.5714, 0.2333) X_647 = CROSSDIFFERENCE OF X(2) AND X(3) (4.2063, -0.5653) X_239 = -LINE CONJUGATE OF X(42) (4.2109, 3.7992) X_514 = ISOGONAL CONJUGATE OF X(101) (1.0761, -0.0329) X_243 = -LINE CONJUGATE OF X(73) (0.7516, 0.9505) X_522 = ISOGONAL CONJUGATE OF X(109) (-0.0318, 0.3430) X_521 = ISOGONAL CONJUGATE OF X(108) (1.1224, 0.1534) X_650 = CROSSDIFFERENCE OF X(1) AND X(3) (13.7143, -4.1991) X_648 = TRILINEAR POLE OF EULER LINE (0.4563, 0.5855) X_1020 = POINT ALGEDI (0.4031, 0.5979) X_333 = CEVAPOINT OF X(8) AND X(9) (0.4886, 0.1475) X_1024 = INTERSECTION OF LINES X(6)X(513) ANDX(9)X(522) (1.0370, 0.0294) X_1021 = ISOGONAL CONJUGATE OF X(1020) (24.7475, -5.0780) A B C X81 X162 X1 X647 X239 X514 X243 X522 X521 X650 X648 X1020 X333 X1024 X1021 (a, b, c) = (5, 6, 7) | AB = 1

X1021 (ISOGONAL CONJUGATE OF X1020) 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 \(f(a,b,c) = (\cos B - \cos C)/(\cos B + \cos C)\)
Barycentrics: \(g(a,b,c) : g(b,c,a) : g(c,a,b)\), where \(g(a,b,c) = af(a,b,c)\)
Search Value (6, 9, 13): \(-52.568162340147\)
▸ Incident Central Lines7 lines

{1, 647}, {239, 514}, {243, 522}, {333, 1024}, {521, 650}, {654, 2596}, {648, 1020}

▸ Functional Relations7 relations