X3538

EULER LINE INTERCEPT OF LINE X1038X_1056

X3538 = {X376,X631}-harmonic conjugate of X24
< 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) { 376, 631 }: Euler Line { 2, 3 }: Euler Line { 1038, 1056 }: Central Line L(1038, 1056) { 1040, 1058 }: Central Line L(1040, 1058) A = Vertex A (0.0000, 0.0000) B = Vertex B (1.0000, 0.0000) C = Vertex C (0.6122, 0.5999) X_24 = PERSPECTOR OF ABC AND ORTHIC-OF-ORTHIC TRIANGLE (0.6627, 0.5278) X_376 = CENTROID OF THE ANTIPEDAL TRIANGLE OF X(2) (0.4626, 0.0042) X_631 = 3/5*OG (0.5224, 0.1608) X_2 = CENTROID (0.5374, 0.2000) X_3 = CIRCUMCENTER (0.5000, 0.1021) X_1038 = INTERSECTION OF LINES X(1)X(3) AND X(2)X(34) (0.5104, 0.1211) X_1056 = POINT ALCYONE (0.5756, 0.2499) X_1040 = INTERSECTION OF LINES X(1)X(3) AND X(2)X(33) (0.4854, 0.0753) X_1058 = POINT ALKALUROPS (0.5662, 0.2123) X_3538 = EULER LINE INTERCEPT OF LINE X(1038)X(1056) (0.4978, 0.0963) A B C X24 X376 X631 X2 X3 X1038 X1056 X1040 X1058 X3538 (a, b, c) = (5, 6, 7) | AB = 1

X3538 (EULER LINE INTERCEPT OF LINE X1038X_1056) 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): \(5.779902146929\)
▸ Incident Central Lines3 lines

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

▸ Functional Relations1 relation

Notes

As a point on the Euler line, X3538 has Shinagawa coefficients \((2E, -2E - F)\).