X926

CROSSDIFFERENCE OF X6 AND X7

As the isogonal conjugate of a point on the circumcircle, X926 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) { 55, 654 }: Central Line L(55, 654) { 101, 692 }: Central Line L(101, 692) { 295, 875 }: Central Line L(295, 875) { 657, 663 }: Central Line L(657, 663) A = Vertex A (0.0000, 0.0000) B = Vertex B (1.0000, 0.0000) C = Vertex C (0.6122, 0.5999) X_927 = ISOGONAL CONJUGATE OF X(926) (1.0037, 0.1836) X_30 = EULER INFINITY POINT (0.7469, 0.7481) X_511 = ISOGONAL CONJUGATE OF X(98) (0.2335, -0.3020) X_55 = INSIMILICENTER(CIRCUMCIRCLE, INCIRCLE) (0.5490, 0.1921) X_654 = CROSSDIFFERENCE OF X(1) AND X(5) (2.8235, 1.7291) X_101 = Ψ(INCENTER, SYMMEDIAN POINT) (0.2143, 0.5249) X_692 = -CEVA CONJUGATE OF X(101) (0.2833, 0.5715) X_295 = ISOGONAL CONJUGATE OF X(242) (1.0582, 0.0142) X_875 = ISOGONAL CONJUGATE OF X(874) (0.9992, -0.0257) X_657 = CROSSDIFFERENCE OF X(1) AND X(7) (10.1538, -2.2611) X_663 = CROSSDIFFERENCE OF X(2) AND X(7) (8.6667, -3.2660) X_926 = CROSSDIFFERENCE OF X(6) AND X(7) (0.0512, -0.1286) A B C X927 X30 X511 X55 X654 X101 X692 X295 X875 X657 X663 X926 (a, b, c) = (5, 6, 7) | AB = 1

X926 (CROSSDIFFERENCE OF X6 AND X7) 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 \(f(a,b,c) = bw - cv\),\(u : v : w\) = X7
▸ Alternate Coordinates1 form

  • Trilinears: \(a (a - b - c) (b - c) (a b + a c - b^{2} - c^{2}) : :\)

▸ Incident Central Lines6 lines

{30, 511}, {55, 654}, {101, 692}, {295, 875}, {657, 663}, {2170, 2310}

▸ Functional Relations8 relations