X1661

2nd GRINBERG MIDPOINTS PERSPECTOR

X1661 is described at X1660.
< 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) { 25, 393 }: Central Line L(25, 393) { 154, 577 }: Central Line L(154, 577) { 1619, 1624 }: Central Line L(1619, 1624) A = Vertex A (0.0000, 0.0000) B = Vertex B (1.0000, 0.0000) C = Vertex C (0.6122, 0.5999) X_20 = DE LONGCHAMPS POINT (0.3878, -0.1916) X_6 = SYMMEDIAN POINT (LEMOINE POINT, GREBE POINT) (0.6000, 0.2672) X_25 = HOMOTHETIC CENTER OF ORTHIC AND TANGENTIAL TRIANGLES (0.6329, 0.4497) X_393 = -CROSS CONJUGATE OF X(4) (0.6247, 0.5263) X_154 = -CEVA CONJUGATE OF X(6) (0.4807, -0.3954) X_577 = HARMONIC OF X(216) (0.4663, 0.0464) X_1619 = TCC-PERSPECTOR OF X(63) (0.4315, -1.6641) X_1624 = TCC-PERSPECTOR OF X(162) (0.4025, 0.6319) X_1661 = 2nd GRINBERG MIDPOINTS PERSPECTOR (0.3740, 2.8798) A B C X20 X6 X25 X393 X154 X577 X1619 X1624 X1661 (a, b, c) = (5, 6, 7) | AB = 1

X1661 (2nd GRINBERG MIDPOINTS PERSPECTOR) 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 \(f(a,b,c) = a(b/v + c/w - a/u)\), where (u,v,w) = (cos A - cos B cos C, cos B - cos C cos A, cos C - cos A cos B).
Barycentrics: \(af(a,b,c) : bf(b,c,a) : cf(c,a,b)\)
Search Value (6, 9, 13): \(-0.937444137137\)
▸ Incident Central Lines3 lines

{25, 393}, {154, 577}, {1619, 1624}

▸ Functional Relations3 relations