X2006

ORTHOCORRESPONDENT OF X80

X2006 = isogonal conjugate of X2323
< 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, 5 }: Feuerbach Line { 7, 89 }: Central Line L(7, 89) { 28, 108 }: Central Line L(28, 108) { 81, 226 }: Central Line L(81, 226) { 274, 349 }: Central Line L(274, 349) { 88, 655 }: Central Line L(88, 655) A = Vertex A (0.0000, 0.0000) B = Vertex B (1.0000, 0.0000) C = Vertex C (0.6122, 0.5999) X_2323 = -ISOCONJUGATE OF X(1411) (-2.1000, -2.9394) X_1 = INCENTER (0.5714, 0.2333) X_5 = NINE-POINT CENTER (0.5561, 0.2489) X_7 = GERGONNE POINT (0.5903, 0.2769) X_89 = ISOGONAL CONJUGATE OF X(45) (0.5963, 0.2697) X_28 = CEVAPOINT OF X(19) AND X(25) (0.6285, 0.4382) X_108 = Ψ(CIRCUMCENTER, INCENTER) (0.5320, 0.6114) X_81 = CEVAPOINT OF INCENTER AND SYMMEDIAN POINT (0.5849, 0.2510) X_226 = -CEVA CONJUGATE OF X(65) (0.5778, 0.2588) X_274 = ISOGONAL CONJUGATE OF X(213) (0.5168, 0.1843) X_349 = ISOTOMIC CONJUGATE OF X(284) (0.5089, 0.1906) X_88 = ISOGONAL CONJUGATE OF X(44) (1.0000, 0.0000) X_655 = TRILINEAR POLE OF LINE X(1)X(5) (1.0449, 0.2400) X_2006 = ORTHOCORRESPONDENT OF X(80) (0.9679, -0.1714) A B C X2323 X1 X5 X7 X89 X28 X108 X81 X226 X274 X349 X88 X655 X2006 (a, b, c) = (5, 6, 7) | AB = 1

X2006 (ORTHOCORRESPONDENT OF X80) 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 \(f(a,b,c) = yz + (-x \cos A + y \cos B + z \cos C)x\), where \(x : y : z\) = X80
Barycentrics: \(af(a,b,c) : bf(b,c,a) : cf(c,a,b)\)
Search Value (6, 9, 13): \(-2.676800198801\)
▸ Alternate Coordinates3 forms

  • Trilinears: \(\sin(A/2) \sec(3A/2) : \sin(B/2) \sec(3B/2) : \sin(C/2) \sec(3C/2)\) (M. Iliev, 4/12/07)

  • Trilinears: \((\tan A/2)/(1 - 2 \cos A) : (\tan B/2)/(1 - 2 \cos B): (\tan C/2)/(1 - 2 \cos C)\) (M. Iliev, 4/12/07)

  • Trilinears: \(g(a,b,c) : g(b,c,a) : g(c,a,b)\), where \(g(a,b,c) = bc/[(b + c - a)(b^{2} + c^{2} - a^{2} - bc)]\) (M. Iliev, 5/13/07)

▸ Incident Central Lines10 lines

{1, 5}, {7, 89}, {28, 108}, {57, 1020}, {79, 1399}, {81, 226}, {88, 655}, {274, 349}, {1427, 1989}, {1758, 1929}

▸ Functional Relations4 relations