X1176

1st SARAGOSSA POINT OF X66

X1176 = X83-Ceva conjugate of X251
< 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) { 6, 22 }: Central Line L(6, 22) { 2, 66 }: Central Line L(2, 66) { 4, 83 }: Central Line L(4, 83) { 65, 82 }: Central Line L(65, 82) { 67, 110 }: Central Line L(67, 110) { 69, 184 }: Central Line L(69, 184) A = Vertex A (0.0000, 0.0000) B = Vertex B (1.0000, 0.0000) C = Vertex C (0.6122, 0.5999) X_427 = COMPLEMENT OF X(22) (0.5990, 0.3610) X_6 = SYMMEDIAN POINT (LEMOINE POINT, GREBE POINT) (0.6000, 0.2672) X_22 = EXETER POINT (0.4143, -0.1221) X_2 = CENTROID (0.5374, 0.2000) X_66 = ISOGONAL CONJUGATE OF X(22) (0.5912, 1.0593) X_4 = ORTHOCENTER (0.6122, 0.3958) X_83 = CEVAPOINT OF CENTROID AND SYMMEDIAN POINT (0.5651, 0.2360) X_65 = ORTHOCENTER OF THE INTOUCH TRIANGLE (0.6041, 0.2933) X_82 = ISOGONAL CONJUGATE OF X(38) (0.5943, 0.2703) X_67 = ISOGONAL CONJUGATE OF X(23) (0.7606, -0.2152) X_110 = FOCUS OF KIEPERT PARABOLA (0.2516, 0.5478) X_69 = SYMMEDIAN POINT OF THE ANTICOMPLEMENTARY TRIANGLE (0.4122, 0.0654) X_184 = INVERSE OF X(125) IN THE BROCARD CIRCLE (0.5788, 0.1496) X_1176 = 1st SARAGOSSA POINT OF X(66) (0.5328, 0.1263) A B C X427 X6 X22 X2 X66 X4 X83 X65 X82 X67 X110 X69 X184 X1176 (a, b, c) = (5, 6, 7) | AB = 1

X1176 (1st SARAGOSSA POINT OF X66) constructed on acute reference triangle \((a, b, c) = (5, 6, 7)\) with unit baseline AB = \(1\).

Constructed Elements

Trilinears: \(a(b^{2} + c^{2} - a^{2})/(b^{2} + c^{2}) : :\) (M. Iliev, 5/13/07)
Search Value (6, 9, 13): \(51.719005423058\)
▸ Alternate Coordinates1 form

  • Trilinears: \(\sin 2A \csc(A + \omega ) : :\)

▸ Incident Central Lines11 lines

{2, 66}, {4, 83}, {6, 22}, {54, 511}, {65, 82}, {67, 110}, {69, 184}, {74, 827}, {216, 248}, {290, 308}, {575, 1173}

▸ Functional Relations6 relations