X1089

TRILINEAR SQUARE OF X10

X1089 = crosspoint of X313 and X321
< 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) { 8, 80 }: Central Line L(8, 80) { 1, 312 }: Central Line L(1, 312) { 10, 321 }: Central Line L(10, 321) { 190, 191 }: Central Line L(190, 191) { 76, 334 }: Central Line L(76, 334) { 200, 318 }: Central Line L(200, 318) A = Vertex A (0.0000, 0.0000) B = Vertex B (1.0000, 0.0000) C = Vertex C (0.6122, 0.5999) X_849 = 4th HATZIPOLAKIS-YIU POINT (0.6376, 0.3351) X_8 = NAGEL POINT (0.4694, 0.1333) X_80 = REFLECTION OF INCENTER IN FEUERBACH POINT (0.8980, -0.1000) X_1 = INCENTER (0.5714, 0.2333) X_312 = ISOTOMIC CONJUGATE OF X(57) (0.4256, 0.1081) X_10 = SPIEKER CENTER (0.5204, 0.1833) X_321 = ISOTOMIC CONJUGATE OF X(81) (0.4800, 0.1527) X_190 = YFF PARABOLIC POINT (0.0748, 0.3999) X_191 = -CEVA CONJUGATE OF X(1) (0.4859, 0.1209) X_76 = 3rd BROCARD POINT (0.4567, 0.1388) X_334 = ISOTOMIC CONJUGATE OF X(238) (1.0545, 0.0278) X_200 = -CEVA CONJUGATE OF X(9) (0.4392, 0.1037) X_318 = ISOTOMIC CONJUGATE OF X(77) (0.5514, 0.2839) X_1089 = TRILINEAR SQUARE OF X(10) (0.4606, 0.1381) A B C X849 X8 X80 X1 X312 X10 X321 X190 X191 X76 X334 X200 X318 X1089 (a, b, c) = (5, 6, 7) | AB = 1

X1089 (TRILINEAR SQUARE OF X10) 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 \(f(a,b,c) = b^{2}c^{2}(b + c)^{2}\)
Barycentrics: \(g(a,b,c) : g(b,c,a) : g(c,a,b)\), where \(g(a,b,c) = af(a,b,c)\)
Search Value (6, 9, 13): \(4.608068085574\)
▸ Incident Central Lines10 lines

{1, 312}, {8, 80}, {10, 321}, {76, 334}, {190, 191}, {200, 318}, {244, 596}, {345, 498}, {594, 762}, {740, 872}

▸ Functional Relations4 relations