X3542

EULER LINE INTERCEPT OF LINE X33X_498

X3542 = inverse-in-orthocentroidal-circle of X3541
< A B C >: Reference Triangle △ABC < K_a K_b K_c >: Anticomplementary Triangle △K_a K_b K_c [ A B ]: Sideline AB (Base c = 1) [ B C ]: Sideline BC (Side a) [ C A ]: Sideline CA (Side b) { 2, 3548 }: Euler Line { 2, 3 }: Euler Line { 33, 498 }: Central Line L(33, 498) { 34, 499 }: Central Line L(34, 499) { 158, 1068 }: Central Line L(158, 1068) { 393, 847 }: Central Line L(393, 847) A = Vertex A (0.0000, 0.0000) B = Vertex B (1.0000, 0.0000) C = Vertex C (0.6122, 0.5999) K_a = Anticomplementary Vertex K_a (1.6122, 0.5999) K_b = Anticomplementary Vertex K_b (-0.3878, 0.5999) K_c = Anticomplementary Vertex K_c (0.3878, -0.5999) X_2 = CENTROID (0.5374, 0.2000) X_3548 = EULER LINE INTERCEPT OF LINE X(68)X(125) (0.4674, 0.0169) X_3 = CIRCUMCENTER (0.5000, 0.1021) X_33 = PERSPECTOR OF THE ORTHIC AND INTANGENTS TRIANGLES (0.6019, 0.3546) X_498 = YFF CONCURRENT CONGRUENT CIRCLES POINT (0.5518, 0.2140) X_34 = -BETH CONJUGATE OF X(4) (0.6332, 0.4792) X_499 = {X(1),X(2)}-HARMONIC CONJUGATE OF X(498) (0.4458, 0.1102) X_158 = -CROSS CONJUGATE OF X(92) (0.6215, 0.5117) X_1068 = -CROSS CONJUGATE OF X(4) (0.6478, 0.5373) X_393 = -CROSS CONJUGATE OF X(4) (0.6247, 0.5263) X_847 = -CROSS CONJUGATE OF X(4) (-0.1806, -0.0821) X_3542 = EULER LINE INTERCEPT OF LINE X(33)X(498) (0.6774, 0.5661) A B C Ka Kb Kc X2 X3548 X3 X33 X498 X34 X499 X158 X1068 X393 X847 X3542 (a, b, c) = (5, 6, 7) | AB = 1

X3542 (EULER LINE INTERCEPT OF LINE X33X_498) 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 \(f(A,B,C) = \sec A - 2 \sin B \sin C\)
Barycentrics: \((\sin A)f(A,B,C) : (\sin B)f(B,C,A) : (\sin C)f(C,A,B)\)
Search Value (6, 9, 13): \(-0.049954881012\)
▸ Incident Central Lines17 lines

{2, 3}, {33, 498}, {34, 499}, {70, 1177}, {107, 1299}, {158, 1068}, {193, 2904}, {206, 1614}, {230, 2207}, {254, 1093}, {393, 847}, {590, 3092}, {615, 3093}, {1300, 1301}, {1352, 1974}, {1870, 3086}, {3186, 3462}

▸ Functional Relations7 relations

Notes

As a point on the Euler line, X3542 has Shinagawa coefficients \((2F, -E)\).