X2257

X2-ISOCONJUGATE OF X939

< 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, 6 }: Incenter–Symmedian Line { 19, 57 }: Central Line L(19, 57) { 58, 84 }: Central Line L(58, 84) { 3, 380 }: Central Line L(3, 380) { 40, 387 }: Central Line L(40, 387) { 56, 610 }: Central Line L(56, 610) 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_6 = SYMMEDIAN POINT (LEMOINE POINT, GREBE POINT) (0.6000, 0.2672) X_19 = CLAWSON POINT (0.6246, 0.4244) X_57 = ISOGONAL CONJUGATE OF X(9) (0.6138, 0.3110) X_58 = ISOGONAL CONJUGATE OF X(10) (0.6107, 0.2850) X_84 = ISOGONAL CONJUGATE OF X(40) (0.6071, 0.6816) X_3 = CIRCUMCENTER (0.5000, 0.1021) X_380 = INTERSECTION OF LINES X(1)X(19) AND X(9)X(55) (0.5631, 0.2035) X_40 = BEVAN POINT (0.4286, -0.0292) X_387 = INTERSECTION OF LINES X(1,2) AND X(4,6) (0.5994, 0.2607) X_56 = EXSIMILICENTER(CIRCUMCIRCLE, INCIRCLE) (0.6316, 0.3438) X_610 = -CEVA CONJUGATE OF X(1) (0.4310, -0.2713) X_2257 = -ISOCONJUGATE OF X(939) (0.6108, 0.2800) A B C X1 X6 X19 X57 X58 X84 X3 X380 X40 X387 X56 X610 X2257 (a, b, c) = (5, 6, 7) | AB = 1

X2257 (X2-ISOCONJUGATE OF X939) constructed on acute reference triangle \((a, b, c) = (5, 6, 7)\) with unit baseline AB = \(1\).

Constructed Elements

Trilinears: \(a/f(a,b,c) : b/f(b,c,a) : c/f(c,a,b)\), where f(a,b,c) is as in X939
Barycentrics: \(a^{2}/f(a,b,c) : b^{2}/f(b,c,a): c^{2}/f(c,a,b)\)
Search Value (6, 9, 13): \(0.879172799086\)
▸ Incident Central Lines20 lines

{1, 6}, {3, 380}, {19, 57}, {40, 387}, {48, 1420}, {56, 610}, {58, 84}, {71, 1697}, {198, 1617}, {281, 1210}, {347, 1445}, {393, 1838}, {604, 1630}, {608, 1394}, {800, 2277}, {1400, 2082}, {1475, 2285}, {1696, 2348}, {1699, 1901}, {1778, 2328}

▸ Functional Relations1 relation