X2832

ISOGONAL CONJUGATE OF X2748

X2832 is the isogonal conjugate of X2748.
< 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) { 105, 106 }: Central Line L(105, 106) { 120, 121 }: Central Line L(120, 121) { 30, 511 }: Central Line L(30, 511) { 659, 764 }: Central Line L(659, 764) { 1292, 1293 }: Central Line L(1292, 1293) { 1054, 1635 }: Central Line L(1054, 1635) A = Vertex A (0.0000, 0.0000) B = Vertex B (1.0000, 0.0000) C = Vertex C (0.6122, 0.5999) X_2748 = SR(X(105), X(106)) (0.6857, -0.3733) X_105 = Λ(INCENTER, SYMMEDIAN POINT) (0.9714, -0.0933) X_106 = Λ(INCENTER, CENTROID) (1.0000, 0.0000) X_120 = -OF-MEDIAL-TRIANGLE (0.3204, 0.3466) X_121 = -OF-MEDIAL-TRIANGLE (0.3061, 0.2999) X_30 = EULER INFINITY POINT (0.7469, 0.7481) X_511 = ISOGONAL CONJUGATE OF X(98) (0.2335, -0.3020) X_659 = CROSSDIFFERENCE OF X(1) AND X(39) (1.9286, 2.2162) X_764 = TRILINEAR CUBE OF X(513) (1.2143, -0.1166) X_1292 = COLLINGS TRANSFORM OF X(55) (0.0286, 0.2974) X_1293 = COLLINGS TRANSFORM OF X(121) (0.0000, 0.2041) X_1054 = 6th SHARYGIN POINT (1.4286, -0.2333) X_1635 = TRIPOLAR CENTROID OF X(1) (2.1429, 2.0996) X_2832 = ISOGONAL CONJUGATE OF X(2748) (0.3656, -0.3612) A B C X2748 X105 X106 X120 X121 X30 X511 X659 X764 X1292 X1293 X1054 X1635 X2832 (a, b, c) = (5, 6, 7) | AB = 1

X2832 (ISOGONAL CONJUGATE OF X2748) 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 \(f(a,b,c) = (b - c)(a^{2} + b^{2} + c^{2} - 3bc)\) (M. Iliev, 5/13/07)
Barycentrics: \(af(a,b,c) : bf(b,c,a) : cf(c,a,b)\)
▸ Incident Central Lines7 lines

{30, 511}, {105, 106}, {120, 121}, {659, 764}, {1054, 1635}, {1292, 1293}, {1357, 1358}

▸ Functional Relations1 relation