X3547

EULER LINE INTERCEPT OF LINE X69X_155

< 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 { 69, 155 }: Central Line L(69, 155) { 68, 1176 }: Central Line L(68, 1176) { 343, 1181 }: Central Line L(343, 1181) { 499, 1038 }: Central Line L(499, 1038) { 498, 1040 }: Central Line L(498, 1040) 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_69 = SYMMEDIAN POINT OF THE ANTICOMPLEMENTARY TRIANGLE (0.4122, 0.0654) X_155 = EIGENCENTER OF ORTHIC TRIANGLE (1.1658, 0.5033) X_68 = PRASOLOV POINT (-0.0535, -0.0055) X_1176 = 1st SARAGOSSA POINT OF X(66) (0.5328, 0.1263) X_343 = ISOTOMIC CONJUGATE OF X(275) (0.4345, 0.0893) X_1181 = 2nd SARAGOSSA POINT OF X(3) (0.5894, 0.1559) X_499 = {X(1),X(2)}-HARMONIC CONJUGATE OF X(498) (0.4458, 0.1102) X_1038 = INTERSECTION OF LINES X(1)X(3) AND X(2)X(34) (0.5104, 0.1211) X_498 = YFF CONCURRENT CONGRUENT CIRCLES POINT (0.5518, 0.2140) X_1040 = INTERSECTION OF LINES X(1)X(3) AND X(2)X(33) (0.4854, 0.0753) X_3547 = EULER LINE INTERCEPT OF LINE X(69)X(155) (0.5071, 0.1205) A B C X2 X3 X4 X69 X155 X68 X1176 X343 X1181 X499 X1038 X498 X1040 X3547 (a, b, c) = (5, 6, 7) | AB = 1

X3547 (EULER LINE INTERCEPT OF LINE X69X_155) 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 \(f(A,B,C) = \sec B \sec C + 2 \sin B \sin C\)
Barycentrics: \((\sin A)f(A,B,C) : (\sin B)f(B,C,A) : (\sin C)f(C,A,B)\)
Search Value (6, 9, 13): \(-80.404228468869\)
▸ Incident Central Lines11 lines

{2, 3}, {68, 1176}, {69, 155}, {343, 1181}, {498, 1040}, {499, 1038}, {577, 2548}, {590, 1579}, {615, 1578}, {1060, 3086}, {1062, 3085}

Notes

As a point on the Euler line, X3547 has Shinagawa coefficients \((E + 2F, -E)\).