X3315

INTERSECTION OF LINES X1X_88 AND X105X_110

X3315 = crosssum of X678 and X2087
< 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) { 1, 88 }: Central Line L(1, 88) { 105, 110 }: Central Line L(105, 110) { 149, 1086 }: Central Line L(149, 1086) { 2, 1280 }: Central Line L(2, 1280) { 291, 1255 }: Central Line L(291, 1255) { 651, 1421 }: Central Line L(651, 1421) A = Vertex A (0.0000, 0.0000) B = Vertex B (1.0000, 0.0000) C = Vertex C (0.6122, 0.5999) X_1 = INCENTER (0.5714, 0.2333) X_88 = ISOGONAL CONJUGATE OF X(44) (1.0000, 0.0000) X_105 = Λ(INCENTER, SYMMEDIAN POINT) (0.9714, -0.0933) X_110 = FOCUS OF KIEPERT PARABOLA (0.2516, 0.5478) X_149 = REFLECTION OF X(20) IN X(104) (1.3265, -0.3333) X_1086 = CENTER OF HYPERBOLA {{A,B,C,X(2),X(7)|} (0.7687, 0.1000) X_2 = CENTROID (0.5374, 0.2000) X_1280 = ISOGONAL CONJUGATE OF X(1279) (1.1600, 0.1306) X_291 = 2nd SHARYGIN POINT (1.0249, 0.0364) X_1255 = ISOGONAL CONJUGATE OF X(1100) (0.5639, 0.2247) X_651 = TRILINEAR POLE OF LINE X(1)X(3) (0.3048, 0.5599) X_1421 = -BETH CONJUGATE OF X(149) (1.7143, -0.9331) X_3315 = INTERSECTION OF LINES X(1)X(88) AND X(105)X(110) (0.6571, 0.1866) A B C X1 X88 X105 X110 X149 X1086 X2 X1280 X291 X1255 X651 X1421 X3315 (a, b, c) = (5, 6, 7) | AB = 1

X3315 (INTERSECTION OF LINES X1X_88 AND X105X_110) 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 \(f(a,b,c) = (a - b)(a - c) + 2(b - c)^{2}\)
Barycentrics: \(af(a,b,c) : bf(b,c,a) : cf(c,a,b)\)
Search Value (6, 9, 13): \(1.484270904162\)
▸ Incident Central Lines8 lines

{1, 88}, {2, 1280}, {105, 110}, {149, 1086}, {291, 1255}, {651, 1421}, {982, 1621}, {1283, 1623}

▸ Functional Relations1 relation