X2810

ISOGONAL CONJUGATE OF X2726

X2810 is the isogonal conjugate of X2726.
< 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) { 43, 57 }: Central Line L(43, 57) { 6, 101 }: Central Line L(6, 101) { 30, 511 }: Central Line L(30, 511) { 1, 3271 }: Central Line L(1, 3271) { 8, 3888 }: Central Line L(8, 3888) { 51, 3873 }: Central Line L(51, 3873) A = Vertex A (0.0000, 0.0000) B = Vertex B (1.0000, 0.0000) C = Vertex C (0.6122, 0.5999) X_2726 = SR(X(101), X(106)) (0.0831, 0.3963) X_43 = -CEVA CONJUGATE OF X(1) (0.6358, 0.2963) X_57 = ISOGONAL CONJUGATE OF X(9) (0.6138, 0.3110) X_6 = SYMMEDIAN POINT (LEMOINE POINT, GREBE POINT) (0.6000, 0.2672) X_101 = Ψ(INCENTER, SYMMEDIAN POINT) (0.2143, 0.5249) X_30 = EULER INFINITY POINT (0.7469, 0.7481) X_511 = ISOGONAL CONJUGATE OF X(98) (0.2335, -0.3020) X_1 = INCENTER (0.5714, 0.2333) X_3271 = CROSSSUM OF X(2) AND X(100) (0.7810, 0.0933) X_8 = NAGEL POINT (0.4694, 0.1333) X_3888 = com[INVERSE(n(3rd EULER TRIANGLE))] (0.0503, 0.4132) X_51 = CENTROID OF ORTHIC TRIANGLE (0.6093, 0.3186) X_3873 = com[INVERSE(n(3rd EULER TRIANGLE))] (0.6272, 0.3066) X_2810 = ISOGONAL CONJUGATE OF X(2726) (0.0494, 0.5260) A B C X2726 X43 X57 X6 X101 X30 X511 X1 X3271 X8 X3888 X51 X3873 X2810 (a, b, c) = (5, 6, 7) | AB = 1

X2810 (ISOGONAL CONJUGATE OF X2726) constructed on acute reference triangle \((a, b, c) = (5, 6, 7)\) with unit baseline AB = \(1\).

Constructed Elements

Trilinears: \(1/f(a,b,c) : 1/f(b,c,a) : 1/f(c,a,b)\), where f(a,b,c) is as at X2726
▸ Alternate Coordinates1 form

  • Trilinears: \(a (a^{2} (b^{2} + c^{2}) - 2 a b c (b + c) - b^{4} + 2 b^{3} c + 2 b c^{3} - c^{4}) : :\)

▸ Incident Central Lines23 lines

{1, 3271}, {6, 101}, {3, 3939}, {8, 3888}, {30, 511}, {43, 57}, {51, 3873}, {100, 3937}, {118, 5480}, {200, 3784}, {210, 3819}, {375, 3742}, {611, 5138}, {1428, 5193}, {1843, 5185}, {2093, 3779}, {2097, 4259}, {2979, 4661}, {3022, 4907}, {3038, 3041}, {3060, 4430}, {3681, 3917}, {3781, 5223}

▸ Functional Relations1 relation