X2635

SUM OF PU(76)

X2635 = bicentric sum of PU(76)
< 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, 4 }: Incenter–Orthocenter Line { 44, 513 }: Central Line L(44, 513) { 11, 1458 }: Central Line L(11, 1458) { 42, 1836 }: Central Line L(42, 1836) { 411, 1935 }: Central Line L(411, 1935) { 971, 1465 }: Central Line L(971, 1465) 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_4 = ORTHOCENTER (0.6122, 0.3958) X_44 = -LINE CONJUGATE OF X(1) (2.1429, 2.0996) X_513 = ISOGONAL CONJUGATE OF X(100) (1.0529, -0.0806) X_11 = FEUERBACH POINT (0.7347, 0.0667) X_1458 = -BETH CONJUGATE OF X(518) (0.8889, 0.9677) X_42 = CROSSPOINT OF INCENTER AND SYMMEDIAN POINT (0.5880, 0.2495) X_1836 = ZOSMA TRANSFORM OF X(33) (0.6066, 0.3254) X_411 = EULER X(21)-2nd-SUBSTITUTION POINT (0.4414, -0.0514) X_1935 = CROSSSUM OF PU(15) (0.5117, 0.2061) X_971 = INTERSECTION OF LINES X(3)X(9) AND X(4)X(7) (0.6441, 0.7770) X_1465 = -BETH CONJUGATE OF X(908) (0.7719, 1.0314) X_2635 = SUM OF PU(76) (1.1729, 2.6275) A B C X1 X4 X44 X513 X11 X1458 X42 X1836 X411 X1935 X971 X1465 X2635 (a, b, c) = (5, 6, 7) | AB = 1

X2635 (SUM OF PU(76)) constructed on acute reference triangle \((a, b, c) = (5, 6, 7)\) with unit baseline AB = \(1\).

Constructed Elements

Trilinears: \(\sec B + \sec C - 2 \sec A : :\)
Search Value (6, 9, 13): \(-4.060048303918\)
▸ Alternate Coordinates1 form

  • Trilinears: \(a^{4} (b + c) - a^{3} (b^{2} + c^{2}) - a^{2} (b - c)^{2} (b + c) + a (b^{2} - c^{2})^{2} - 2 b c (b - c)^{2} (b + c) : :\)

▸ Incident Central Lines18 lines

{1, 4}, {11, 1458}, {42, 1836}, {44, 513}, {209, 2390}, {329, 2318}, {411, 1935}, {651, 1936}, {774, 1898}, {823, 2659}, {908, 1818}, {971, 1465}, {1042, 1837}, {1044, 1788}, {1156, 1937}, {1254, 1858}, {1427, 1864}, {1758, 1776}

▸ Functional Relations3 relations