X2610

SUM OF PU(71)

X2610 = crossdifference of every pair of points on line X1X60
< 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) { 115, 125 }: Central Line L(115, 125) { 44, 513 }: Central Line L(44, 513) { 918, 1211 }: Central Line L(918, 1211) { 1213, 1639 }: Central Line L(1213, 1639) { 1983, 2613 }: Central Line L(1983, 2613) { 2611, 2615 }: Central Line L(2611, 2615) A = Vertex A (0.0000, 0.0000) B = Vertex B (1.0000, 0.0000) C = Vertex C (0.6122, 0.5999) X_523 = ISOGONAL CONJUGATE OF X(110) (1.0856, -0.0096) X_115 = CENTER OF KIEPERT HYPERBOLA (0.7507, 0.0838) X_125 = CENTER OF JERABEK HYPERBOLA (0.6803, 0.0260) X_44 = -LINE CONJUGATE OF X(1) (2.1429, 2.0996) X_513 = ISOGONAL CONJUGATE OF X(100) (1.0529, -0.0806) X_918 = ISOTOMIC CONJUGATE OF X(666) (1.0192, 0.5351) X_1211 = ISOGONAL CONJUGATE OF X(1169) (0.5137, 0.1744) X_1213 = ISOGONAL CONJUGATE OF X(1171) (0.5294, 0.1914) X_1639 = TRIPOLAR CENTROID OF X(8) (-0.6122, -0.5999) X_1983 = VEGA TRANSFORM OF X(523) (0.9661, 0.8719) X_2613 = CROSSDIFFERENCE OF PU(70) (0.2669, 0.5328) X_2611 = DIFFERENCE OF PU(71) (0.7448, 0.0628) X_2615 = MIDPOINT OF PU(71) (0.6849, 0.0131) X_2610 = SUM OF PU(71) (2.7813, 1.7520) A B C X523 X115 X125 X44 X513 X918 X1211 X1213 X1639 X1983 X2613 X2611 X2615 X2610 (a, b, c) = (5, 6, 7) | AB = 1

X2610 (SUM OF PU(71)) 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 \(f(A,B,C) = \csc(C - A) + \csc(B - A)\),
Barycentrics: \((\sin A)f(A,B,C) : (\sin B)f(B,C,A) : (\sin C)f(C,A,B)\)
Search Value (6, 9, 13): \(-10.461618074219\)
▸ Incident Central Lines6 lines

{44, 513}, {115, 125}, {918, 1211}, {1213, 1639}, {1983, 2613}, {2611, 2615}

▸ Functional Relations8 relations

Notes

X2610 is the perspector of triangle ABC and the tangential triangle of the hyperbola that passes through the points A, B, C, X1, and X12. (Randy Hutson, 9/23/2011)