X1816

INVERSE MIMOSA TRANSFORM OF X1075

X1816 = X283-Ceva conjugate of X21
< 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 A = Vertex A (0.0000, 0.0000) B = Vertex B (1.0000, 0.0000) C = Vertex C (0.6122, 0.5999) X_283 = -CROSS CONJUGATE OF X(21) (0.4475, 0.0704) X_21 = SCHIFFLER POINT (0.5287, 0.1771) X_2 = CENTROID (0.5374, 0.2000) X_3 = CIRCUMCENTER (0.5000, 0.1021) X_1816 = INVERSE MIMOSA TRANSFORM OF X(1075) (0.4215, -0.1035) A B C X283 X21 X2 X3 X1816 (a, b, c) = (5, 6, 7) | AB = 1

X1816 (INVERSE MIMOSA TRANSFORM OF X1075) 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 \(f(a,b,c) = (\cos A)/(y + z)\),\(x : y : z\) = X1075
Barycentrics: \(af(a,b,c) : bf(b,c,a) : cf(c,a,b)\)
Search Value (6, 9, 13): \(5.832081494731\)
▸ Incident Central Lines1 line

{2, 3}

▸ Functional Relations1 relation

Notes

As a point on the Euler line, X1816 has Shinagawa coefficients \((4EF^{3}abc - \$aS_{A}\$[S^{2} - (2E + 3F)F][S^{2} - (2E + F)F] + 2\$aS_{B}S_{C}\$[S^{2} - (2E + F)F]F + 4\$a(S_{A})^{3}\$F^{2}, [S^{4} - (2E - F)FS^{2} + F^{4}]abc + \$aS_{A}\$[S^{2} - (2E + 3F)F][S^{2} - (2E + F)F] - 2\$aS_{B}S_{C}\$[S^{2} - (2E + F)F]F - 4\$a(S_{A})^{3}\$F^{2})\).