X1474

X1172-BETH CONJUGATE OF X1172

X1474 = isogonal conjugate of X306
< 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, 19 }: Central Line L(1, 19) { 6, 25 }: Central Line L(6, 25) { 27, 86 }: Central Line L(27, 86) { 106, 112 }: Central Line L(106, 112) { 4, 572 }: Central Line L(4, 572) { 24, 573 }: Central Line L(24, 573) A = Vertex A (0.0000, 0.0000) B = Vertex B (1.0000, 0.0000) C = Vertex C (0.6122, 0.5999) X_1172 = 1st SARAGOSSA POINT OF X(48) (0.6100, 0.3717) X_1 = INCENTER (0.5714, 0.2333) X_19 = CLAWSON POINT (0.6246, 0.4244) X_6 = SYMMEDIAN POINT (LEMOINE POINT, GREBE POINT) (0.6000, 0.2672) X_25 = HOMOTHETIC CENTER OF ORTHIC AND TANGENTIAL TRIANGLES (0.6329, 0.4497) X_27 = CEVAPOINT OF ORTHOCENTER AND CLAWSON CENTER (0.6182, 0.4112) X_86 = CEVAPOINT OF INCENTER AND CENTROID (0.5534, 0.2171) X_106 = Λ(INCENTER, CENTROID) (1.0000, 0.0000) X_112 = Ψ(ORTHOCENTER, SYMMEDIAN POINT) (0.5162, 0.6121) X_4 = ORTHOCENTER (0.6122, 0.3958) X_572 = ORTHOGONAL OF X(58) (7.2953, -0.6907) X_24 = PERSPECTOR OF ABC AND ORTHIC-OF-ORTHIC TRIANGLE (0.6627, 0.5278) X_573 = ORTHOHARMONIC OF X(58) (0.4583, 0.2009) X_1474 = -BETH CONJUGATE OF X(1172) (0.6165, 0.3951) A B C X1172 X1 X19 X6 X25 X27 X86 X106 X112 X4 X572 X24 X573 X1474 (a, b, c) = (5, 6, 7) | AB = 1

X1474 (X1172-BETH CONJUGATE OF X1172) 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 \(u : v : w\) = X1172
Barycentrics: \(af(a,b,c) : bf(b,c,a) : cf(c,a,b)\)
Search Value (6, 9, 13): \(-0.345378719510\)
▸ Incident Central Lines17 lines

{1, 19}, {4, 572}, {6, 25}, {24, 573}, {27, 86}, {29, 1220}, {34, 604}, {56, 608}, {106, 112}, {163, 913}, {198, 939}, {269, 1396}, {281, 996}, {286, 870}, {459, 966}, {468, 1213}, {1408, 1413}

▸ Functional Relations7 relations