X1375

EVANS POINT

X1375 = complement of X857
< A B C >: Reference Triangle △ABC < M_a M_b M_c >: Medial Triangle △M_a M_b M_c [ A B ]: Sideline AB (Base c = 1) [ B C ]: Sideline BC (Side a) [ C A ]: Sideline CA (Side b) { 2, 857 }: Euler Line { 2, 3 }: Euler Line { 241, 514 }: Central Line L(241, 514) A = Vertex A (0.0000, 0.0000) B = Vertex B (1.0000, 0.0000) C = Vertex C (0.6122, 0.5999) M_a = Midpoint M_a of BC (0.8061, 0.2999) M_b = Midpoint M_b of CA (0.3061, 0.2999) M_c = Midpoint M_c of AB (0.5000, 0.0000) X_2 = CENTROID (0.5374, 0.2000) X_857 = INTERCEPT OF EULER LINE AND TRILINEAR POLAR OF X(75) (-0.3133, -2.0259) X_3 = CIRCUMCENTER (0.5000, 0.1021) X_241 = -LINE CONJUGATE OF X(55) (1.1217, 1.2442) X_514 = ISOGONAL CONJUGATE OF X(101) (1.0761, -0.0329) X_1375 = EVANS POINT (0.9628, 1.3129) A B C Ma Mb Mc X2 X857 X3 X241 X514 X1375 (a, b, c) = (5, 6, 7) | AB = 1

X1375 (EVANS POINT) 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 \(f(a,b,c) = bc[- 2a^{2}\cos A + b(a - b + c)\cos B + c(a + b - c)\cos C]\)
Barycentrics: \(g(a,b,c) : g(b,c,a) : g(c,a,b)\), where \(g(a,b,c) = - 2a^{2}\cos A + b(a - b + c)\cos B + c(a + b - c)\cos C\)
Search Value (6, 9, 13): \(-0.205710989599\)
▸ Incident Central Lines2 lines

{2, 3}, {241, 514}

▸ Functional Relations2 relations

Notes

As a point on the Euler line, X1375 has Shinagawa coefficients \((2\$aS_{B}S_{C}\$ - \$a\$S^{2}, \$a\$S^{2}). Adrian Oldknow, "The Euler-Gergonne-Soddy Triangle of a Triangle," American Mathematical Monthly 103 (1996) 319-329. See page 328\).

See also MathWorld, Evans Point.