X1583

POINT CAPELLA I

X1583 = inverse-in-orthocentroidal-circle of X1591
< 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) { 2, 3 }: Euler Line { 6, 493 }: Central Line L(6, 493) { 371, 394 }: Central Line L(371, 394) A = Vertex A (0.0000, 0.0000) B = Vertex B (1.0000, 0.0000) C = Vertex C (0.6122, 0.5999) X_2 = CENTROID (0.5374, 0.2000) X_3 = CIRCUMCENTER (0.5000, 0.1021) X_4 = ORTHOCENTER (0.6122, 0.3958) X_6 = SYMMEDIAN POINT (LEMOINE POINT, GREBE POINT) (0.6000, 0.2672) X_493 = 1st VAN LAMOEN HOMOTHETIC CENTER (0.5707, 0.2293) X_371 = KENMOTU POINT (CONGRUENT SQUARES POINT) (0.5652, 0.2097) X_394 = -CEVA CONJUGATE OF X(3) (0.3778, 0.0284) X_1583 = POINT CAPELLA I (0.5270, 0.1728) A B C X2 X3 X4 X6 X493 X371 X394 X1583 (a, b, c) = (5, 6, 7) | AB = 1

X1583 (POINT CAPELLA I) 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 \(f(A,B,C) = \csc A + \cos A\)
Barycentrics: \((\sin A)f(A,B,C) : (\sin B)f(B,C,A) : (\sin C)f(C,A,B)\)
Search Value (6, 9, 13): \(3.150278525621\)
▸ Linear Combinations1 combination
▸ Incident Central Lines3 lines

{2, 3}, {6, 493}, {371, 394}

▸ Functional Relations1 relation

  • X1583 = inverse-in-orthocentroidal-circle of X1591

Notes

As a point on the Euler line, X1583 has Shinagawa coefficients \((E + S, -S)\).