X3031

INTERSECTION X10X_125∩X74X_573

X3031 = complement of X38482
< 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) { 10, 125 }: Central Line L(10, 125) { 110, 386 }: Central Line L(110, 386) { 74, 573 }: Central Line L(74, 573) { 113, 2051 }: Central Line L(113, 2051) { 43, 2948 }: Central Line L(43, 2948) { 1017, 2092 }: Central Line L(1017, 2092) A = Vertex A (0.0000, 0.0000) B = Vertex B (1.0000, 0.0000) C = Vertex C (0.6122, 0.5999) X_10 = SPIEKER CENTER (0.5204, 0.1833) X_125 = CENTER OF JERABEK HYPERBOLA (0.6803, 0.0260) X_110 = FOCUS OF KIEPERT PARABOLA (0.2516, 0.5478) X_386 = INVERSE-IN-BROCARD-CIRCLE OF X(58) (0.5912, 0.2526) X_74 = ISOGONAL CONJUGATE OF EULER INFINITY POINT (0.7484, -0.3437) X_573 = ORTHOHARMONIC OF X(58) (0.4486, 0.0172) X_113 = JERABEK ANTIPODE (0.4319, 0.4718) X_2051 = EXSIMILICENTER(NINE-POINT CIRCLE, APOLLONIUS CIRCLE) (0.6034, 0.3358) X_43 = -CEVA CONJUGATE OF X(1) (0.6358, 0.2963) X_2948 = EXCENTRAL-ISOGONAL CONJUGATE OF X(30) (-0.0682, 0.8624) X_1017 = POINT ALFIRK (0.4054, 0.3972) X_2092 = DANNEELS-APOLLONIUS PERSPECTOR (0.5833, 0.2396) X_3031 = INTERSECTION X(10)X(125)∩X(74)X(573) (-0.6264, 1.3112) A B C X10 X125 X110 X386 X74 X573 X113 X2051 X43 X2948 X1017 X2092 X3031 (a, b, c) = (5, 6, 7) | AB = 1

X3031 (INTERSECTION X10X_125∩X74X_573) 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 \(f(a,b,c) = a(b + c)^{2}(a^{3} + b^{3} - c^{3} + a^{2}c - b^{2}c - ac^{2})(a^{3} - b^{3} + c^{3} + a^{2}b - bc^{2} - ab^{2})\)
Barycentrics: \(af(a,b,c) : bf(b,c,a) : cf(c,a,b)\)
Search Value (6, 9, 13): \(-0.005322676294\)

X3031 lies on the Apollonius circle.

▸ Incident Central Lines10 lines

{10, 125}, {43, 2948}, {74, 573}, {110, 386}, {113, 2051}, {690, 3029}, {1017, 2092}, {2774, 3033}, {2836, 3034}, {2842, 3030}

▸ Functional Relations1 relation

  • X3031 = complement of X38482