X1060

INTERSECTION OF LINES X1X_3 AND X5X_34

X1060 = homothetic center of 2nd Euler triangle and anti-tangential midarc triangle
< 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) { 1, 3 }: OI Line (Incenter–Circumcenter Line) { 5, 34 }: Central Line L(5, 34) { 30, 33 }: Central Line L(30, 33) { 68, 73 }: Central Line L(68, 73) { 201, 255 }: Central Line L(201, 255) { 72, 394 }: Central Line L(72, 394) A = Vertex A (0.0000, 0.0000) B = Vertex B (1.0000, 0.0000) C = Vertex C (0.6122, 0.5999) X_1061 = ISOGONAL CONJUGATE OF X(1060) (0.6067, 0.3472) X_1 = INCENTER (0.5714, 0.2333) X_3 = CIRCUMCENTER (0.5000, 0.1021) X_5 = NINE-POINT CENTER (0.5561, 0.2489) X_34 = -BETH CONJUGATE OF X(4) (0.6332, 0.4792) X_30 = EULER INFINITY POINT (0.7469, 0.7481) X_33 = PERSPECTOR OF THE ORTHIC AND INTANGENTS TRIANGLES (0.6019, 0.3546) X_68 = PRASOLOV POINT (-0.0535, -0.0055) X_73 = CROSSPOINT OF INCENTER AND CIRCUMCENTER (0.5487, 0.1428) X_201 = -CEVA CONJUGATE OF X(12) (0.4897, 0.1062) X_255 = ISOGONAL CONJUGATE OF X(158) (0.4217, 0.0365) X_72 = ISOGONAL CONJUGATE OF X(28) (0.4367, 0.0733) X_394 = -CEVA CONJUGATE OF X(3) (0.3778, 0.0284) X_1060 = INTERSECTION OF LINES X(1)X(3) AND X(5)X(34) (0.5181, 0.1353) A B C X1061 X1 X3 X5 X34 X30 X33 X68 X73 X201 X255 X72 X394 X1060 (a, b, c) = (5, 6, 7) | AB = 1

X1060 (INTERSECTION OF LINES X1X_3 AND X5X_34) 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 \(f(A,B,C) = 2 + \sec B \sec C\)
Barycentrics: \(g(A,B,C) : g(B,C,A) : g(C,A,B)\), where \(g(A,B,C) = (\sin A) f(A,B,C)\)
Search Value (6, 9, 13): \(-0.768081627118\)
▸ Incident Central Lines14 lines

{1, 3}, {5, 34}, {21, 1063}, {30, 33}, {68, 73}, {72, 394}, {141, 997}, {201, 255}, {216, 1015}, {222, 912}, {377, 1068}, {495, 612}, {601, 774}, {976, 1066}

▸ Functional Relations2 relations