X1414

X99-BETH CONJUGATE OF X99

X1414 = trilinear pole of line X57X77
< 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) { 99, 109 }: Central Line L(99, 109) { 85, 603 }: Central Line L(85, 603) { 7, 757 }: Central Line L(7, 757) { 162, 658 }: Central Line L(162, 658) { 110, 934 }: Central Line L(110, 934) { 163, 1019 }: Central Line L(163, 1019) A = Vertex A (0.0000, 0.0000) B = Vertex B (1.0000, 0.0000) C = Vertex C (0.6122, 0.5999) X_99 = STEINER POINT (0.1109, 0.4322) X_109 = Ψ(INCENTER, CIRCUMCENTER) (0.3636, 0.5938) X_85 = ISOTOMIC CONJUGATE OF X(9) (0.5610, 0.2421) X_603 = -CEVA CONJUGATE OF X(56) (0.5992, 0.1851) X_7 = GERGONNE POINT (0.5903, 0.2769) X_757 = ISOGONAL CONJUGATE OF X(756) (0.5971, 0.2688) X_162 = CEVAPOINT OF X(108) AND X(109) (0.4897, 0.6018) X_658 = TRILINEAR POLE OF LINE X(1)X(7) (0.3795, 0.5837) X_110 = FOCUS OF KIEPERT PARABOLA (0.2516, 0.5478) X_934 = -CROSS CONJUGATE OF X(57) (0.4269, 0.6071) X_163 = TRILINEAR PRODUCT X(6)*X(110) (0.3174, 0.5883) X_1019 = -CEVA CONJUGATE OF X(1) (-29.0952, 18.1962) X_1414 = -BETH CONJUGATE OF X(99) (0.3368, 0.5766) A B C X99 X109 X85 X603 X7 X757 X162 X658 X110 X934 X163 X1019 X1414 (a, b, c) = (5, 6, 7) | AB = 1

X1414 (X99-BETH CONJUGATE OF X99) 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 \(f(a,b,c) = (1 - \cos A)u(a,b,c)\), where \(u : v : w\) = X99
Barycentrics: \(af(a,b,c) : bf(b,c,a) : cf(c,a,b)\)
Search Value (6, 9, 13): \(0.236820856428\)
▸ Incident Central Lines10 lines

{7, 757}, {58, 1416}, {85, 603}, {99, 109}, {110, 934}, {162, 658}, {163, 1019}, {348, 1098}, {651, 662}, {1014, 1122}

▸ Functional Relations5 relations