X1565

ORTHOJOIN OF X657

X1565 = midpoint of X150 and X664
< 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) { 150, 664 }: Central Line L(150, 664) { 5, 85 }: Central Line L(5, 85) { 7, 104 }: Central Line L(7, 104) { 4, 279 }: Central Line L(4, 279) { 3, 348 }: Central Line L(3, 348) A = Vertex A (0.0000, 0.0000) B = Vertex B (1.0000, 0.0000) C = Vertex C (0.6122, 0.5999) X_150 = REFLECTION OF X(20) IN X(103) (1.1837, -0.4499) X_664 = TRILINEAR POLE OF LINE X(2)X(7) (0.2391, 0.5142) X_5 = NINE-POINT CENTER (0.5561, 0.2489) X_85 = ISOTOMIC CONJUGATE OF X(9) (0.5610, 0.2421) X_7 = GERGONNE POINT (0.5903, 0.2769) X_104 = ANTIPODE OF X(100) (0.8571, -0.2624) X_4 = ORTHOCENTER (0.6122, 0.3958) X_279 = ISOGONAL CONJUGATE OF X(220) (0.6236, 0.3540) X_3 = CIRCUMCENTER (0.5000, 0.1021) X_348 = ISOTOMIC CONJUGATE OF X(281) (0.4854, 0.1069) X_1565 = ORTHOJOIN OF X(657) (0.7114, 0.0321) A B C X150 X664 X5 X85 X7 X104 X4 X279 X3 X348 X1565 (a, b, c) = (5, 6, 7) | AB = 1

X1565 (ORTHOJOIN OF X657) 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 \(f(a,b,c) = bc(b - c)^{2}(b^{2} + c^{2} - a^{2})\) (M. Iliev, 5/13/07)
Search Value (6, 9, 13): \(2.990353879146\)
▸ Incident Central Lines14 lines

{3, 348}, {4, 279}, {5, 85}, {7, 104}, {11, 1111}, {77, 1060}, {84, 738}, {116, 514}, {150, 664}, {304, 337}, {515, 1323}, {812, 1015}, {1119, 1440}, {1364, 1367}

▸ Functional Relations6 relations