X928

CROSSDIFFERENCE OF X6 AND X11

As the isogonal conjugate of a point on the circumcircle, X928 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) { 102, 103 }: Central Line L(102, 103) { 101, 109 }: Central Line L(101, 109) { 117, 118 }: Central Line L(117, 118) { 116, 124 }: Central Line L(116, 124) { 151, 152 }: Central Line L(151, 152) { 30, 511 }: Central Line L(30, 511) A = Vertex A (0.0000, 0.0000) B = Vertex B (1.0000, 0.0000) C = Vertex C (0.6122, 0.5999) X_929 = ISOGONAL CONJUGATE OF X(928) (0.9516, 0.3396) X_102 = Λ(INCENTER, ORTHOCENTER) (0.6364, -0.3897) X_103 = ANTIPODE OF X(101) (0.7857, -0.3208) X_101 = Ψ(INCENTER, SYMMEDIAN POINT) (0.2143, 0.5249) X_109 = Ψ(INCENTER, CIRCUMCENTER) (0.3636, 0.5938) X_117 = MIDPOINT OF X(4) AND X(109) (0.4879, 0.4948) X_118 = MIDPOINT OF X(4) AND X(101) (0.4133, 0.4603) X_116 = MIDPOINT OF X(4) AND X(103) (0.6990, 0.0375) X_124 = -OF-MEDIAL-TRIANGLE (0.6243, 0.0030) X_151 = REFLECTION OF X(20) IN X(109) (0.3395, 1.3793) X_152 = REFLECTION OF X(20) IN X(101) (0.0408, 1.2414) X_30 = EULER INFINITY POINT (0.7469, 0.7481) X_511 = ISOGONAL CONJUGATE OF X(98) (0.2335, -0.3020) X_928 = CROSSDIFFERENCE OF X(6) AND X(11) (1.0703, 0.4459) A B C X929 X102 X103 X101 X109 X117 X118 X116 X124 X151 X152 X30 X511 X928 (a, b, c) = (5, 6, 7) | AB = 1

X928 (CROSSDIFFERENCE OF X6 AND X11) 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 \(f(a,b,c) = bw - cv\),\(u : v : w\) = X11
Barycentrics: \(g(a,b,c) : g(b,c,a) : g(c,a,b)\), where \(g(a,b,c) = af(a,b,c)\)
▸ Incident Central Lines7 lines

{30, 511}, {101, 109}, {102, 103}, {116, 124}, {117, 118}, {151, 152}, {295, 876}

▸ Functional Relations6 relations