X1197

3rd SARAGOSSA POINT OF X31

X1197 = crosssum of X37 and X75
< 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, 43 }: Central Line L(6, 43) { 31, 32 }: Central Line L(31, 32) { 81, 239 }: Central Line L(81, 239) { 284, 893 }: Central Line L(284, 893) A = Vertex A (0.0000, 0.0000) B = Vertex B (1.0000, 0.0000) C = Vertex C (0.6122, 0.5999) X_1221 = ISOGONAL CONJUGATE OF X(1197) (0.5249, 0.1927) X_6 = SYMMEDIAN POINT (LEMOINE POINT, GREBE POINT) (0.6000, 0.2672) X_43 = -CEVA CONJUGATE OF X(1) (0.6358, 0.2963) X_31 = 2nd POWER POINT (0.6228, 0.3008) X_32 = 3rd POWER POINT (0.6400, 0.3332) X_81 = CEVAPOINT OF INCENTER AND SYMMEDIAN POINT (0.5849, 0.2510) X_239 = -LINE CONJUGATE OF X(42) (4.2109, 3.7992) X_284 = -CROSS CONJUGATE OF X(21) (0.5646, 0.2088) X_893 = -CROSS CONJUGATE OF X(292) (0.5910, 0.2480) X_1197 = 3rd SARAGOSSA POINT OF X(31) (0.6088, 0.2744) A B C X1221 X6 X43 X31 X32 X81 X239 X284 X893 X1197 (a, b, c) = (5, 6, 7) | AB = 1

X1197 (3rd SARAGOSSA POINT OF X31) 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 \(f(a,b,c) = a^{2}(ab^{2} + ac^{2} + b^{2}c + bc^{2})\) (M. Iliev, 5/13/07)
Search Value (6, 9, 13): \(0.823752025731\)
▸ Incident Central Lines4 lines

{6, 43}, {31, 32}, {81, 239}, {284, 893}

▸ Functional Relations4 relations