X2664

CROSSDIFFERENCE OF PU(84)

X2664 = perspector of conic {{A, B, C,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, 2 }: Nagel Line { 171, 213 }: Central Line L(171, 213) { 86, 872 }: Central Line L(86, 872) { 37, 1045 }: Central Line L(37, 1045) { 274, 1215 }: Central Line L(274, 1215) { 101, 1580 }: Central Line L(101, 1580) A = Vertex A (0.0000, 0.0000) B = Vertex B (1.0000, 0.0000) C = Vertex C (0.6122, 0.5999) X_2 = CENTROID (0.5374, 0.2000) X_1 = INCENTER (0.5714, 0.2333) X_171 = {X(2), X(31)}-HARMONIC CONJUGATE OF X(238) (0.5819, 0.2525) X_213 = -CEVA CONJUGATE OF X(42) (0.6135, 0.2833) 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_37 = CROSSPOINT OF INCENTER AND CENTROID (0.5567, 0.2158) X_1045 = -CEVA CONJUGATE OF X(1) (0.6065, 0.2647) X_274 = ISOGONAL CONJUGATE OF X(213) (0.5168, 0.1843) X_1215 = ISOGONAL CONJUGATE OF X(1178) (0.5340, 0.2011) X_101 = Ψ(INCENTER, SYMMEDIAN POINT) (0.2143, 0.5249) X_1580 = POINT ALUDRA (1.3094, 1.2033) X_2664 = CROSSDIFFERENCE OF PU(84) (1.9947, 1.6278) A B C X2 X1 X171 X213 X86 X872 X37 X1045 X274 X1215 X101 X1580 X2664 (a, b, c) = (5, 6, 7) | AB = 1

X2664 (CROSSDIFFERENCE 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): \(-5.505284132721\)
▸ Incident Central Lines14 lines

{1, 2}, {9, 1740}, {37, 1045}, {86, 872}, {87, 1743}, {101, 1580}, {171, 213}, {190, 2234}, {238, 2110}, {274, 1215}, {292, 2238}, {660, 1757}, {980, 984}, {1376, 2176}

▸ Functional Relations3 relations