X1321

1st YIU SQUARES PERSPECTOR

Let \(BB_{A}\)CAC be the external square on side BC, and define \(CC_{B}\)ABA and \(AA_{C}\)BCB cyclically. Let X = BCB∩CBC and X' = BAB∩CAC, and define Y, Z and Y', Z' cyclically. The lines AX, BY, CZ concur in X4, and the lines AX', BY', CZ' concur in X485. The lines XX', YY', ZZ' concur in X1321, as shown in
< 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) { 4, 371 }: Central Line L(4, 371) A = Vertex A (0.0000, 0.0000) B = Vertex B (1.0000, 0.0000) C = Vertex C (0.6122, 0.5999) X_4 = ORTHOCENTER (0.6122, 0.3958) X_371 = KENMOTU POINT (CONGRUENT SQUARES POINT) (0.5652, 0.2097) X_1321 = 1st YIU SQUARES PERSPECTOR (0.6050, 0.3673) A B C X4 X371 X1321 (a, b, c) = (5, 6, 7) | AB = 1

X1321 (1st YIU SQUARES PERSPECTOR) 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 \(f(A,B,C) = (2 \cos A + \sin A)/(\cos^{2} A + \cos A \sin A)\)
Barycentrics: \((\sin A)f(A,B,C) : (\sin B)f(B,C,A) : (\sin C)f(C,A,B)\)
Search Value (6, 9, 13): \(2.520605065308\)
▸ Linear Combinations1 combination
▸ Incident Central Lines2 lines

{4, 371}, {1322, 2165}