X2047

EULER LINE INTERCEPT OF LINE X10X_485

< 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 { 10, 485 }: Central Line L(10, 485) { 86, 637 }: Central Line L(86, 637) { 492, 1330 }: Central Line L(492, 1330) { 590, 1834 }: Van Aubel Line { 966, 1587 }: Central Line L(966, 1587) 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_10 = SPIEKER CENTER (0.5204, 0.1833) X_485 = VECTEN POINT (0.5773, 0.2578) X_86 = CEVAPOINT OF INCENTER AND CENTROID (0.5534, 0.2171) X_637 = ANTICOMPLEMENT OF X(371) (0.4819, 0.1805) X_492 = CEVAPOINT OF X(2) AND X(488) (0.4893, 0.1483) X_1330 = ANTICOMPLEMENTARY CONJUGATE OF X(1) (0.3908, 0.0300) X_590 = ISOGONAL CONJUGATE OF X(588) (0.6000, 0.2672) X_1834 = ZOSMA TRANSFORM OF X(28) (0.5987, 0.2534) X_966 = INTERSECTION OF LINES X(2)X(6) AND X(4)X(9) (0.5191, 0.1803) X_1587 = POINT CASTOR I (0.6026, 0.2943) X_2047 = EULER LINE INTERCEPT OF LINE X(10)X(485) (0.5417, 0.2111) A B C X2 X3 X4 X10 X485 X86 X637 X492 X1330 X590 X1834 X966 X1587 X2047 (a, b, c) = (5, 6, 7) | AB = 1

X2047 (EULER LINE INTERCEPT OF LINE X10X_485) 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 \(f(A,B,C) = (s - r)\cos A + (s + r)\cos(B -C)\), where r = inradius, s = semiperimeter
Barycentrics: \((\sin A)f(A,B,C) : (\sin B)f(B,C,A) : (\sin C)f(C,A,B)\)
Search Value (6, 9, 13): \(2.308023326671\)
▸ Incident Central Lines6 lines

{2, 3}, {10, 485}, {86, 637}, {492, 1330}, {590, 1834}, {966, 1587}

Notes

As a point on the Euler line, X2047 has Shinagawa coefficients \((s,r)\).