X2663

CROSSSUM OF PU(84)

X2663 = crosspoint of PU(85)
< 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, 6 }: Incenter–Symmedian Line { 42, 894 }: Central Line L(42, 894) { 86, 872 }: Central Line L(86, 872) { 314, 1215 }: Central Line L(314, 1215) { 291, 2092 }: Central Line L(291, 2092) { 190, 2665 }: Central Line L(190, 2665) A = Vertex A (0.0000, 0.0000) B = Vertex B (1.0000, 0.0000) C = Vertex C (0.6122, 0.5999) X_1 = INCENTER (0.5714, 0.2333) X_6 = SYMMEDIAN POINT (LEMOINE POINT, GREBE POINT) (0.6000, 0.2672) X_42 = CROSSPOINT OF INCENTER AND SYMMEDIAN POINT (0.5880, 0.2495) X_894 = ISOGONAL CONJUGATE OF X(893) (0.5501, 0.2184) X_86 = CEVAPOINT OF INCENTER AND CENTROID (0.5534, 0.2171) X_872 = INTERSECTION OF LINES X(37)X(42) AND X(43)X(75) (0.6029, 0.2656) X_314 = ISOTOMIC CONJUGATE OF X(65) (0.4457, 0.1206) X_1215 = ISOGONAL CONJUGATE OF X(1178) (0.5340, 0.2011) X_291 = 2nd SHARYGIN POINT (1.0249, 0.0364) X_2092 = DANNEELS-APOLLONIUS PERSPECTOR (0.5833, 0.2396) X_190 = YFF PARABOLIC POINT (0.0748, 0.3999) X_2665 = TRILINEAR POLE OF PU(84) (1.0458, 0.0952) X_2663 = CROSSSUM OF PU(84) (0.5786, 0.2418) A B C X1 X6 X42 X894 X86 X872 X314 X1215 X291 X2092 X190 X2665 X2663 (a, b, c) = (5, 6, 7) | AB = 1

X2663 (CROSSSUM OF PU(84)) 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 \(f(a,b,c) = (1/a + 1/b)(1/a + 1/c) + (1/b + 1/c)^{2}\)
Barycentrics: \(af(a,b,c) : bf(b,c,a) : cf(c,a,b)\)
Search Value (6, 9, 13): \(1.513874483725\)
▸ Incident Central Lines6 lines

{1, 6}, {42, 894}, {86, 872}, {190, 2665}, {291, 2092}, {314, 1215}

▸ Functional Relations1 relation

  • X2663 = crosspoint of PU(85)