X3745

X81com[n(MEDIAL)*n(INCENTRAL)]

X3745 = complement of X33075
< 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) { 31, 37 }: Central Line L(31, 37) { 6, 210 }: Central Line L(6, 210) { 81, 518 }: Central Line L(81, 518) { 33, 608 }: Central Line L(33, 608) { 44, 756 }: Central Line L(44, 756) A = Vertex A (0.0000, 0.0000) B = Vertex B (1.0000, 0.0000) C = Vertex C (0.6122, 0.5999) X_1 = INCENTER (0.5714, 0.2333) X_3 = CIRCUMCENTER (0.5000, 0.1021) X_31 = 2nd POWER POINT (0.6228, 0.3008) X_37 = CROSSPOINT OF INCENTER AND CENTROID (0.5567, 0.2158) X_6 = SYMMEDIAN POINT (LEMOINE POINT, GREBE POINT) (0.6000, 0.2672) X_210 = -CEVA CONJUGATE OF X(37) (0.4925, 0.1466) X_81 = CEVAPOINT OF INCENTER AND SYMMEDIAN POINT (0.5849, 0.2510) X_518 = ISOGONAL CONJUGATE OF X(105) (0.9154, 0.6489) X_33 = PERSPECTOR OF THE ORTHIC AND INTANGENTS TRIANGLES (0.6019, 0.3546) X_608 = ISOGONAL CONJUGATE OF X(345) (0.6361, 0.4975) X_44 = -LINE CONJUGATE OF X(1) (2.1429, 2.0996) X_756 = CROSSPOINT OF X(10) AND X(37) (0.5409, 0.1988) X_3745 = com[n(MEDIAL)*n(INCENTRAL)] (0.5741, 0.2381) A B C X1 X3 X31 X37 X6 X210 X81 X518 X33 X608 X44 X756 X3745 (a, b, c) = (5, 6, 7) | AB = 1

X3745 (X81com[n(MEDIAL)*n(INCENTRAL)]) constructed on acute reference triangle \((a, b, c) = (5, 6, 7)\) with unit baseline AB = \(1\).

Constructed Elements

Barycentrics: \(f(a,b,c) : f(b,c,a) : f(c,a,b)\), where \(f(a,b,c) = a(2a^{2} + b^{2} + c^{2} + ab + ac + 2bc)\)
Search Value (6, 9, 13): \(1.609753961152\)
▸ Incident Central Lines16 lines

{1, 3}, {2, 1386}, {6, 210}, {31, 37}, {33, 608}, {42, 1100}, {44, 756}, {81, 518}, {197, 2262}, {200, 1449}, {226, 1456}, {238, 1961}, {902, 1962}, {968, 3052}, {1279, 2239}, {2194, 2303}

▸ Functional Relations1 relation

  • X3745 = complement of X33075