X3189

X27-CEVA CONJUGATE OF X9

X3189 = reflection of X2550 in X3174
< 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) { 2550, 3174 }: Central Line L(2550, 3174) { 8, 21 }: Central Line L(8, 21) { 1, 142 }: Central Line L(1, 142) { 65, 145 }: Central Line L(65, 145) { 40, 476 }: Central Line L(40, 476) A = Vertex A (0.0000, 0.0000) B = Vertex B (1.0000, 0.0000) C = Vertex C (0.6122, 0.5999) X_2550 = INSIMILICENTER(SPIEKER CIRCLE, (X(4),2R)) (0.5298, 0.2051) X_3174 = -CEVA CONJUGATE OF X(9) (0.7534, 0.3567) X_8 = NAGEL POINT (0.4694, 0.1333) X_21 = SCHIFFLER POINT (0.5287, 0.1771) X_1 = INCENTER (0.5714, 0.2333) X_142 = COMPLEMENT OF X(9) (0.5506, 0.2192) X_65 = ORTHOCENTER OF THE INTOUCH TRIANGLE (0.6041, 0.2933) X_145 = ANTICOMPLEMENT OF NAGEL POINT (0.6735, 0.3333) X_40 = BEVAN POINT (0.4286, -0.0292) X_476 = TIXIER POINT (0.9824, 0.2685) X_3189 = -CEVA CONJUGATE OF X(9) (0.9770, 0.5082) A B C X2550 X3174 X8 X21 X1 X142 X65 X145 X40 X476 X3189 (a, b, c) = (5, 6, 7) | AB = 1

X3189 (X27-CEVA CONJUGATE OF X9) constructed on acute reference triangle \((a, b, c) = (5, 6, 7)\) with unit baseline AB = \(1\).

Constructed Elements

Trilinears: \(u(-u/x + v/y + w/z) : v(u/x - v/y + w/z) : w(u/x + v/y - w/z)\), where \(x : y : z\) = X27 and \(u : v : w\) = X9
Barycentrics: \(af(a,b,c) : bf(b,c,a) : cf(c,a,b)\), where \(f(a,b,c) = u(-u/x + v/y + w/z)\)
Search Value (6, 9, 13): \(-15.663525520969\)
▸ Alternate Coordinates1 form

  • Barycentrics: \(g(a,b,c) : g(b,c,a) : g(c,a,b)\), where \(g(a,b,c) = (b + c - a)[3a^{3} + a^{2}(b + c) - a(b + c)^{2} + (b + c)(b - c)^{2}] (E\). Danneels)

▸ Incident Central Lines19 lines

{1, 142}, {4, 2900}, {8, 21}, {20, 518}, {40, 476}, {65, 145}, {71, 3169}, {78, 497}, {100, 1788}, {200, 950}, {210, 452}, {281, 2332}, {346, 2264}, {380, 2321}, {390, 960}, {528, 962}, {938, 1376}, {997, 1058}, {1118, 1897}

▸ Functional Relations4 relations