X931

POINT ALCHIBA

X931 = trilinear pole of line X6X21
< 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) { 101, 643 }: Central Line L(101, 643) { 100, 645 }: Central Line L(100, 645) { 108, 648 }: Central Line L(108, 648) { 109, 662 }: Central Line L(109, 662) { 111, 941 }: Central Line L(111, 941) A = Vertex A (0.0000, 0.0000) B = Vertex B (1.0000, 0.0000) C = Vertex C (0.6122, 0.5999) X_101 = Ψ(INCENTER, SYMMEDIAN POINT) (0.2143, 0.5249) X_643 = TRILINEAR MULTIPLIER FOR KIEPERT PARABOLA (0.0142, 0.3704) X_100 = ANTICOMPLEMENT OF FEUERBACH POINT (0.1429, 0.4666) X_645 = BARYCENTRIC MULTIPLIER FOR KIEPERT PARABOLA (-0.0375, 0.2992) X_108 = Ψ(CIRCUMCENTER, INCENTER) (0.5320, 0.6114) X_648 = TRILINEAR POLE OF EULER LINE (0.4563, 0.5855) X_109 = Ψ(INCENTER, CIRCUMCENTER) (0.3636, 0.5938) X_662 = TRILINEAR POLE OF LINE X(1)X(21) (0.1811, 0.4951) X_111 = PARRY POINT (0.9885, -0.0457) X_941 = ISOGONAL CONJUGATE OF X(940) (0.5671, 0.2256) X_931 = POINT ALCHIBA (0.1633, 0.4855) A B C X101 X643 X100 X645 X108 X648 X109 X662 X111 X941 X931 (a, b, c) = (5, 6, 7) | AB = 1

X931 (POINT ALCHIBA) 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 \(f(a,b,c) = 1/(bw - cv)\),\(u : v : w\) = X21
Barycentrics: \(g(a,b,c) : g(b,c,a) : g(c,a,b)\), where \(g(a,b,c) = af(a,b,c)\)
Search Value (6, 9, 13): \(2.172567017455\)

X931 lies on the circumcircle.

▸ Incident Central Lines5 lines

{100, 645}, {101, 643}, {108, 648}, {109, 662}, {111, 941}

▸ Functional Relations3 relations