X918

ISOTOMIC CONJUGATE OF X666

As the isogonal conjugate of a point of the circumcircle, X918 lies on the line at infinity.
< 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) { 30, 511 }: Central Line L(30, 511) { 63, 654 }: Central Line L(63, 654) { 190, 644 }: Central Line L(190, 644) { 1086, 1111 }: Central Line L(1086, 1111) A = Vertex A (0.0000, 0.0000) B = Vertex B (1.0000, 0.0000) C = Vertex C (0.6122, 0.5999) X_666 = TRILINEAR POLE OF LINE X(2)X(11) (1.0982, 0.1428) X_30 = EULER INFINITY POINT (0.7469, 0.7481) X_511 = ISOGONAL CONJUGATE OF X(98) (0.2335, -0.3020) X_63 = ISOGONAL CONJUGATE OF X(19) (0.4566, 0.0823) X_654 = CROSSDIFFERENCE OF X(1) AND X(5) (2.8235, 1.7291) X_190 = YFF PARABOLIC POINT (0.0748, 0.3999) X_644 = TRILINEAR MULTIPLIER FOR YFF PARABOLA (-0.0171, 0.3359) X_1086 = CENTER OF HYPERBOLA {{A,B,C,X(2),X(7)|} (0.7687, 0.1000) X_1111 = TRILINEAR SQUARE OF X(514) (0.7470, 0.0849) X_918 = ISOTOMIC CONJUGATE OF X(666) (1.0192, 0.5351) A B C X666 X30 X511 X63 X654 X190 X644 X1086 X1111 X918 (a, b, c) = (5, 6, 7) | AB = 1

X918 (ISOTOMIC CONJUGATE OF X666) 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 \(f(a,b,c) = (w/b - v/c)/a^{2}\),\(u : v : w\) = X100
Barycentrics: \(g(a,b,c) : g(b,c,a) : g(c,a,b)\), where \(g(a,b,c) = (b - c)(b^{2} + c^{2} -ab - ac)\)
▸ Incident Central Lines4 lines

{30, 511}, {63, 654}, {190, 644}, {1086, 1111}

▸ Functional Relations7 relations