X1477

X1280-BETH CONJUGATE OF X1280

X1477 = Λ(X8, X9)
< 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) { 56, 101 }: Central Line L(56, 101) { 57, 100 }: Central Line L(57, 100) { 1, 1292 }: Central Line L(1, 1292) { 55, 1293 }: Central Line L(55, 1293) { 109, 1407 }: Central Line L(109, 1407) { 110, 1412 }: Central Line L(110, 1412) A = Vertex A (0.0000, 0.0000) B = Vertex B (1.0000, 0.0000) C = Vertex C (0.6122, 0.5999) X_1280 = ISOGONAL CONJUGATE OF X(1279) (1.1600, 0.1306) X_56 = EXSIMILICENTER(CIRCUMCIRCLE, INCIRCLE) (0.6316, 0.3438) X_101 = Ψ(INCENTER, SYMMEDIAN POINT) (0.2143, 0.5249) X_57 = ISOGONAL CONJUGATE OF X(9) (0.6138, 0.3110) X_100 = ANTICOMPLEMENT OF FEUERBACH POINT (0.1429, 0.4666) X_1 = INCENTER (0.5714, 0.2333) X_1292 = COLLINGS TRANSFORM OF X(55) (0.0286, 0.2974) X_55 = INSIMILICENTER(CIRCUMCIRCLE, INCIRCLE) (0.5490, 0.1921) X_1293 = COLLINGS TRANSFORM OF X(121) (0.0000, 0.2041) X_109 = Ψ(INCENTER, CIRCUMCENTER) (0.3636, 0.5938) X_1407 = -BETH CONJUGATE OF X(57) (0.6456, 0.4125) X_110 = FOCUS OF KIEPERT PARABOLA (0.2516, 0.5478) X_1412 = -BETH CONJUGATE OF X(81) (0.6374, 0.3603) X_1477 = -BETH CONJUGATE OF X(1280) (1.0040, 0.1822) A B C X1280 X56 X101 X57 X100 X1 X1292 X55 X1293 X109 X1407 X110 X1412 X1477 (a, b, c) = (5, 6, 7) | AB = 1

X1477 (X1280-BETH CONJUGATE OF X1280) 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 \(u : v : w\) = X1280
Barycentrics: \(af(a,b,c) : bf(b,c,a) : cf(c,a,b)\)
Search Value (6, 9, 13): \(-0.570306529176\)

X1477 lies on the circumcircle.

▸ Incident Central Lines11 lines

{1, 1292}, {55, 1293}, {56, 101}, {57, 100}, {99, 1434}, {108, 1435}, {109, 1407}, {110, 1412}, {738, 934}, {919, 1416}, {1308, 1319}

▸ Functional Relations6 relations