X1390

ISOGONAL CONJUGATE OF X1386

X1390 is the isogonal conjugate of X1386.
< 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) { 38, 57 }: Central Line L(38, 57) { 37, 105 }: Central Line L(37, 105) { 81, 518 }: Central Line L(81, 518) { 279, 388 }: Central Line L(279, 388) { 278, 427 }: Central Line L(278, 427) { 984, 985 }: Central Line L(984, 985) 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_984 = MIDPOINT OF X(8) AND X(192) (0.5421, 0.1984) X_38 = CROSSPOINT OF X(1) AND X(75) (0.5443, 0.1976) X_57 = ISOGONAL CONJUGATE OF X(9) (0.6138, 0.3110) X_37 = CROSSPOINT OF INCENTER AND CENTROID (0.5567, 0.2158) X_105 = Λ(INCENTER, SYMMEDIAN POINT) (0.9714, -0.0933) X_81 = CEVAPOINT OF INCENTER AND SYMMEDIAN POINT (0.5849, 0.2510) X_518 = ISOGONAL CONJUGATE OF X(105) (0.9154, 0.6489) X_279 = ISOGONAL CONJUGATE OF X(220) (0.6236, 0.3540) X_388 = ∩X(7)X(8) (0.5790, 0.2635) X_278 = ISOGONAL CONJUGATE OF X(219) (0.6278, 0.4577) X_427 = COMPLEMENT OF X(22) (0.5990, 0.3610) X_985 = ISOGONAL CONJUGATE OF X(984) (0.5961, 0.2693) X_1390 = ISOGONAL CONJUGATE OF X(1386) (0.5559, 0.2165) A B C X1 X984 X38 X57 X37 X105 X81 X518 X279 X388 X278 X427 X985 X1390 (a, b, c) = (5, 6, 7) | AB = 1

X1390 (ISOGONAL CONJUGATE OF X1386) 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 \(f(a,b,c) = 1/[a(a + b + c) + (a^{2} + b^{2} + c^{2})]\)
Barycentrics: \(af(a,b,c) : bf(b,c,a) : cf(c,a,b)\)
Search Value (6, 9, 13): \(2.087279604498\)
▸ Incident Central Lines6 lines

{37, 105}, {38, 57}, {81, 518}, {278, 427}, {279, 388}, {984, 985}

▸ Functional Relations2 relations