X2868

SM(X110, X111)

X2868 = isogonal conjugate of X2882
< 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) { 112, 385 }: Central Line L(112, 385) { 76, 691 }: Central Line L(76, 691) { 69, 805 }: Central Line L(69, 805) { 111, 850 }: Central Line L(111, 850) { 669, 2373 }: Central Line L(669, 2373) A = Vertex A (0.0000, 0.0000) B = Vertex B (1.0000, 0.0000) C = Vertex C (0.6122, 0.5999) X_2882 = ISOGONAL CONJUGATE OF X(2868) (0.9382, -0.2287) X_112 = Ψ(ORTHOCENTER, SYMMEDIAN POINT) (0.5162, 0.6121) X_385 = -HIRST INVERSE OF X(6) (2.2863, 2.0795) X_76 = 3rd BROCARD POINT (0.4567, 0.1388) X_691 = TRILINEAR POLE OF LINE X(6)X(110) (1.0101, 0.0886) X_69 = SYMMEDIAN POINT OF THE ANTICOMPLEMENTARY TRIANGLE (0.4122, 0.0654) X_805 = o-(- 2, 2) CIRCUMCIRCLE POINT (0.9729, -0.0897) X_111 = PARRY POINT (0.9885, -0.0457) X_850 = BARYCENTRIC MULTIPLIER FOR KIEPERT HYPERBOLA (-6.8003, 1.7304) X_669 = CROSSDIFFERENCE OF X(2) AND X(39) (-4.3514, 4.6163) X_2373 = CIR(X(67)) (0.5684, -0.4036) X_2868 = SM(X(110), X(111)) (-0.0042, 0.1807) A B C X2882 X112 X385 X76 X691 X69 X805 X111 X850 X669 X2373 X2868 (a, b, c) = (5, 6, 7) | AB = 1

X2868 (SM(X110, X111)) 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) is given just before X2855 using P = X110 and U = X111
Barycentrics: \(af(a,b,c) : bf(b,c,a) : cf(c,a,b)\)
Search Value (6, 9, 13): \(8.715380224390\)

X2868 lies on the circumcircle.

▸ Incident Central Lines6 lines

{69, 805}, {76, 691}, {110, 3266}, {111, 850}, {112, 385}, {669, 2373}

▸ Functional Relations1 relation