X2748

SR(X105, X106)

X2748 = isogonal conjugate of X2832
< 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, 519 }: Central Line L(105, 519) { 106, 518 }: Central Line L(106, 518) { 901, 1026 }: Central Line L(901, 1026) { 919, 1023 }: Central Line L(919, 1023) { 1083, 2382 }: Central Line L(1083, 2382) A = Vertex A (0.0000, 0.0000) B = Vertex B (1.0000, 0.0000) C = Vertex C (0.6122, 0.5999) X_2832 = ISOGONAL CONJUGATE OF X(2748) (0.3656, -0.3612) X_105 = Λ(INCENTER, SYMMEDIAN POINT) (0.9714, -0.0933) X_519 = ISOGONAL CONJUGATE OF X(106) (0.9566, 0.6107) X_106 = Λ(INCENTER, CENTROID) (1.0000, 0.0000) X_518 = ISOGONAL CONJUGATE OF X(105) (0.9154, 0.6489) X_901 = ISOGONAL CONJUGATE OF X(900) (1.0000, -0.0000) X_1026 = INTERSECTION OF LINES X(1)X(2) AND X(100)X(101) (4.1429, 3.7326) X_919 = ISOGONAL CONJUGATE OF X(918) (1.0058, 0.1699) X_1023 = INTERSECTION OF LINES X(1)X(6) AND X(100)X(101) (2.1429, 2.0996) X_1083 = MIDPOINT OF X(105) AND X(644) (0.4771, 0.1213) X_2382 = CIR(X(537)) (0.2893, 0.5668) X_2748 = SR(X(105), X(106)) (0.6857, -0.3733) A B C X2832 X105 X519 X106 X518 X901 X1026 X919 X1023 X1083 X2382 X2748 (a, b, c) = (5, 6, 7) | AB = 1

X2748 (SR(X105, X106)) 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 \(f(a,b,c) = 1/[(b - c)(a^{2} + b^{2} + c^{2} - 3bc)]\) (M. Iliev, 5/13/07)
Barycentrics: \(af(a,b,c) : bf(b,c,a) : cf(c,a,b)\)
Search Value (6, 9, 13): \(14.159440951463\)

X2748 lies on the circumcircle.

▸ Incident Central Lines5 lines

{105, 519}, {106, 518}, {901, 1026}, {919, 1023}, {1083, 2382}

▸ Functional Relations1 relation