X1062

INTERSECTION OF LINES X1X_3 AND X5X_33

X1062 = homothetic center of intangents triangle and 2nd Euler 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, 33 }: Central Line L(5, 33) { 30, 34 }: Central Line L(30, 34) { 21, 1061 }: Central Line L(21, 1061) { 496, 614 }: Central Line L(496, 614) { 602, 774 }: Central Line L(602, 774) A = Vertex A (0.0000, 0.0000) B = Vertex B (1.0000, 0.0000) C = Vertex C (0.6122, 0.5999) X_1063 = ISOGONAL CONJUGATE OF X(1062) (0.6152, 0.5187) X_1 = INCENTER (0.5714, 0.2333) X_3 = CIRCUMCENTER (0.5000, 0.1021) X_5 = NINE-POINT CENTER (0.5561, 0.2489) X_33 = PERSPECTOR OF THE ORTHIC AND INTANGENTS TRIANGLES (0.6019, 0.3546) X_30 = EULER INFINITY POINT (0.7469, 0.7481) X_34 = -BETH CONJUGATE OF X(4) (0.6332, 0.4792) X_21 = SCHIFFLER POINT (0.5287, 0.1771) X_1061 = ISOGONAL CONJUGATE OF X(1060) (0.6067, 0.3472) X_496 = {X(1),X(5)}-HARMONIC CONJUGATE OF X(495) (0.5843, 0.2201) X_614 = INTERSECTION OF LINES X(1)X(2) AND X(11)X(33) (0.6310, 0.2916) X_602 = INTERSECTION OF LINES X(3)X(31) AND X(56)X(255) (0.8182, 0.6170) X_774 = CROSSPOINT OF X(1) AND X(158) (0.6363, 0.3186) X_1062 = INTERSECTION OF LINES X(1)X(3) AND X(5)X(33) (0.4633, 0.0347) A B C X1063 X1 X3 X5 X33 X30 X34 X21 X1061 X496 X614 X602 X774 X1062 (a, b, c) = (5, 6, 7) | AB = 1

X1062 (INTERSECTION OF LINES X1X_3 AND X5X_33) 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): \(2.941029167978\)
▸ Incident Central Lines7 lines

{1, 3}, {5, 33}, {21, 1061}, {30, 34}, {394, 1069}, {496, 614}, {602, 774}

▸ Functional Relations2 relations