X1178

1st SARAGOSSA POINT OF X82

X1178 = isogonal conjugate of X1215
< 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) { 21, 238 }: Central Line L(21, 238) { 6, 694 }: Central Line L(6, 694) { 82, 662 }: Central Line L(82, 662) { 284, 893 }: Central Line L(284, 893) { 765, 872 }: Central Line L(765, 872) { 741, 985 }: Central Line L(741, 985) A = Vertex A (0.0000, 0.0000) B = Vertex B (1.0000, 0.0000) C = Vertex C (0.6122, 0.5999) X_1215 = ISOGONAL CONJUGATE OF X(1178) (0.5340, 0.2011) X_21 = SCHIFFLER POINT (0.5287, 0.1771) X_238 = -LINE CONJUGATE OF X(37) (1.6190, 1.4775) X_6 = SYMMEDIAN POINT (LEMOINE POINT, GREBE POINT) (0.6000, 0.2672) X_694 = ISOGONAL CONJUGATE OF X(385) (1.0179, 0.0378) X_82 = ISOGONAL CONJUGATE OF X(38) (0.5943, 0.2703) X_662 = TRILINEAR POLE OF LINE X(1)X(21) (0.1811, 0.4951) X_284 = -CROSS CONJUGATE OF X(21) (0.5646, 0.2088) X_893 = -CROSS CONJUGATE OF X(292) (0.5910, 0.2480) X_765 = CEVAPOINT OF X(1) AND X(100) (0.4286, 0.3110) X_872 = INTERSECTION OF LINES X(37)X(42) AND X(43)X(75) (0.6029, 0.2656) X_741 = EVEN (- 1, 1) CIRCUMCIRCLE POINT (1.0071, 0.0451) X_985 = ISOGONAL CONJUGATE OF X(984) (0.5961, 0.2693) X_1178 = 1st SARAGOSSA POINT OF X(82) (0.6029, 0.2656) A B C X1215 X21 X238 X6 X694 X82 X662 X284 X893 X765 X872 X741 X985 X1178 (a, b, c) = (5, 6, 7) | AB = 1

X1178 (1st SARAGOSSA POINT OF X82) 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 \(f(a,b,c) = a/[(b + c)(a^{2} + bc)]\) (M. Iliev, 5/13/07)
Search Value (6, 9, 13): \(0.958356606936\)
▸ Incident Central Lines10 lines

{6, 694}, {21, 238}, {82, 662}, {284, 893}, {409, 1201}, {604, 1169}, {741, 985}, {759, 995}, {765, 872}, {869, 983}

▸ Functional Relations3 relations