X2701

SR(X98, X102)

X2701 = reflection of X2708 in X3
< 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) { 2708, 3 }: Central Line L(2708, 3) { 98, 515 }: Central Line L(98, 515) { 102, 511 }: Central Line L(102, 511) { 99, 522 }: Central Line L(99, 522) { 109, 512 }: Central Line L(109, 512) A = Vertex A (0.0000, 0.0000) B = Vertex B (1.0000, 0.0000) C = Vertex C (0.6122, 0.5999) X_2708 = SR(X(98), X(109)) (0.0010, -0.0050) X_3 = CIRCUMCENTER (0.5000, 0.1021) X_98 = TARRY POINT (0.8891, -0.2281) X_515 = ISOGONAL CONJUGATE OF X(102) (0.6804, 0.7691) X_102 = Λ(INCENTER, ORTHOCENTER) (0.6364, -0.3897) X_511 = ISOGONAL CONJUGATE OF X(98) (0.2335, -0.3020) X_99 = STEINER POINT (0.1109, 0.4322) X_522 = ISOGONAL CONJUGATE OF X(109) (-0.0318, 0.3430) X_109 = Ψ(INCENTER, CIRCUMCENTER) (0.3636, 0.5938) X_512 = ISOGONAL CONJUGATE OF X(99) (1.0394, -0.1040) X_2701 = SR(X(98), X(102)) (0.9990, 0.2091) A B C X2708 X3 X98 X515 X102 X511 X99 X522 X109 X512 X2701 (a, b, c) = (5, 6, 7) | AB = 1

X2701 (SR(X98, X102)) 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 \(f(a,b,c) = a/[(b - c)(a^{3} + b^{3} + c^{3} - 2a^{2}b - 2a^{2}c + abc)]\) (M. Iliev, 5/13/07)
Barycentrics: \(af(a,b,c) : bf(b,c,a) : cf(c,a,b)\)
Search Value (6, 9, 13): \(-0.550398168205\)

X2701 lies on the circumcircle.

▸ Incident Central Lines14 lines

{3, 2708}, {98, 515}, {99, 522}, {102, 511}, {104, 2648}, {109, 512}, {110, 663}, {111, 1055}, {187, 2291}, {759, 1326}, {953, 1064}, {991, 2700}, {1951, 2249}, {1983, 2702}

▸ Functional Relations4 relations