X1167

1st SARAGOSSA POINT OF X34

X1167 = isogonal conjugate of X1210
< 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) { 34, 40 }: Central Line L(34, 40) { 255, 269 }: Central Line L(255, 269) { 56, 580 }: Central Line L(56, 580) { 31, 937 }: Central Line L(31, 937) { 271, 936 }: Central Line L(271, 936) { 595, 998 }: Central Line L(595, 998) A = Vertex A (0.0000, 0.0000) B = Vertex B (1.0000, 0.0000) C = Vertex C (0.6122, 0.5999) X_1210 = ISOGONAL CONJUGATE OF X(1167) (0.6144, 0.2754) X_34 = -BETH CONJUGATE OF X(4) (0.6332, 0.4792) X_40 = BEVAN POINT (0.4286, -0.0292) X_255 = ISOGONAL CONJUGATE OF X(158) (0.4217, 0.0365) X_269 = ISOGONAL CONJUGATE OF X(200) (0.6369, 0.3847) X_56 = EXSIMILICENTER(CIRCUMCIRCLE, INCIRCLE) (0.6316, 0.3438) X_580 = ORTHOGONAL OF X(284) (0.7089, 0.4470) X_31 = 2nd POWER POINT (0.6228, 0.3008) X_937 = ISOGONAL CONJUGATE OF X(936) (0.6143, 0.2920) X_271 = ISOGONAL CONJUGATE OF X(208) (1.1546, 2.8606) X_936 = INTERSECTION OF LINES X(1)X(2) AND X(3)X(9) (0.5138, 0.1768) X_595 = 2nd HATZIPOLAKIS-YIU POINT (0.6456, 0.3307) X_998 = ISOGONAL CONJUGATE OF X(997) (0.6186, 0.3014) X_1167 = 1st SARAGOSSA POINT OF X(34) (0.5172, 0.1910) A B C X1210 X34 X40 X255 X269 X56 X580 X31 X937 X271 X936 X595 X998 X1167 (a, b, c) = (5, 6, 7) | AB = 1

X1167 (1st SARAGOSSA POINT OF X34) 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): \(2.189842007645\)
▸ Incident Central Lines6 lines

{31, 937}, {34, 40}, {56, 580}, {255, 269}, {271, 936}, {595, 998}

▸ Functional Relations3 relations