X1170

1st SARAGOSSA POINT OF X41

X1170 = isogonal conjugate of X1212
< 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) { 41, 57 }: Central Line L(41, 57) { 65, 105 }: Central Line L(65, 105) { 2, 220 }: Central Line L(2, 220) { 7, 218 }: Central Line L(7, 218) { 6, 279 }: Central Line L(6, 279) { 81, 241 }: Central Line L(81, 241) A = Vertex A (0.0000, 0.0000) B = Vertex B (1.0000, 0.0000) C = Vertex C (0.6122, 0.5999) X_1212 = ISOGONAL CONJUGATE OF X(1170) (0.5256, 0.1789) X_41 = -CEVA CONJUGATE OF X(31) (0.5823, 0.2244) X_57 = ISOGONAL CONJUGATE OF X(9) (0.6138, 0.3110) X_65 = ORTHOCENTER OF THE INTOUCH TRIANGLE (0.6041, 0.2933) X_105 = Λ(INCENTER, SYMMEDIAN POINT) (0.9714, -0.0933) X_2 = CENTROID (0.5374, 0.2000) X_220 = -CEVA CONJUGATE OF X(55) (0.4826, 0.1278) X_7 = GERGONNE POINT (0.5903, 0.2769) X_218 = -CEVA CONJUGATE OF X(55) (0.6557, 0.3333) X_6 = SYMMEDIAN POINT (LEMOINE POINT, GREBE POINT) (0.6000, 0.2672) X_279 = ISOGONAL CONJUGATE OF X(220) (0.6236, 0.3540) X_81 = CEVAPOINT OF INCENTER AND SYMMEDIAN POINT (0.5849, 0.2510) X_241 = -LINE CONJUGATE OF X(55) (1.1217, 1.2442) X_1170 = 1st SARAGOSSA POINT OF X(41) (0.6064, 0.2908) A B C X1212 X41 X57 X65 X105 X2 X220 X7 X218 X6 X279 X81 X241 X1170 (a, b, c) = (5, 6, 7) | AB = 1

X1170 (1st SARAGOSSA POINT OF X41) constructed on acute reference triangle \((a, b, c) = (5, 6, 7)\) with unit baseline AB = \(1\).

Constructed Elements

Trilinears: \(f(a,b,c) : f(b,c,a) : f(c,a,b)\) (see note above X1166)
Search Value (6, 9, 13): \(0.559757640305\)
▸ Alternate Coordinates1 form

  • Trilinears: \(1/((a - b - c) (a (b + c) - (b - c)^{2})) : :\)

▸ Incident Central Lines9 lines

{2, 220}, {3, 955}, {6, 279}, {7, 218}, {41, 57}, {56, 1002}, {65, 105}, {81, 241}, {278, 607}

▸ Functional Relations4 relations