X3537

EULER LINE INTERCEPT OF LINE X1038X_1058

< 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 { 577, 1285 }: Central Line L(577, 1285) { 1038, 1058 }: Central Line L(1038, 1058) { 1040, 1056 }: Central Line L(1040, 1056) 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_577 = HARMONIC OF X(216) (0.4663, 0.0464) X_1285 = LEMOINE HOMOTHETIC CENTER (0.6375, 0.3389) X_1038 = INTERSECTION OF LINES X(1)X(3) AND X(2)X(34) (0.5104, 0.1211) X_1058 = POINT ALKALUROPS (0.5662, 0.2123) X_1040 = INTERSECTION OF LINES X(1)X(3) AND X(2)X(33) (0.4854, 0.0753) X_1056 = POINT ALCYONE (0.5756, 0.2499) X_3537 = EULER LINE INTERCEPT OF LINE X(1038)X(1058) (0.5021, 0.1076) A B C X2 X3 X4 X577 X1285 X1038 X1058 X1040 X1056 X3537 (a, b, c) = (5, 6, 7) | AB = 1

X3537 (EULER LINE INTERCEPT OF LINE X1038X_1058) 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 \(f(A,B,C) = \cos B \cos C + 2 \sec B \sec C\)
Barycentrics: \((\sin A)f(A,B,C) : (\sin B)f(B,C,A) : (\sin C)f(C,A,B)\)
Search Value (6, 9, 13): \(7.977079563448\)
▸ Incident Central Lines4 lines

{2, 3}, {577, 1285}, {1038, 1058}, {1040, 1056}

Notes

As a point on the Euler line, X3537 has Shinagawa coefficients \((2E, -2E + F)\).