X3293

SS(a → b + c) OF X3

X3293 = reflection of X1 in X1193
< 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) { 1, 1193 }: Nagel Line { 1, 2 }: Nagel Line { 58, 100 }: Central Line L(58, 100) { 40, 209 }: Central Line L(40, 209) { 71, 380 }: Central Line L(71, 380) A = Vertex A (0.0000, 0.0000) B = Vertex B (1.0000, 0.0000) C = Vertex C (0.6122, 0.5999) X_1 = INCENTER (0.5714, 0.2333) X_1193 = 3rd SARAGOSSA POINT OF X(1) (0.5959, 0.2573) X_2 = CENTROID (0.5374, 0.2000) X_58 = ISOGONAL CONJUGATE OF X(10) (0.6107, 0.2850) X_100 = ANTICOMPLEMENT OF FEUERBACH POINT (0.1429, 0.4666) X_40 = BEVAN POINT (0.4286, -0.0292) X_209 = -CEVA CONJUGATE OF X(37) (0.7303, 0.4592) X_71 = ISOGONAL CONJUGATE OF X(27) (0.4807, 0.0915) X_380 = INTERSECTION OF LINES X(1)X(19) AND X(9)X(55) (0.5631, 0.2035) X_3293 = SS(a → b + c) OF X(3) (0.6204, 0.2812) A B C X1 X1193 X2 X58 X100 X40 X209 X71 X380 X3293 (a, b, c) = (5, 6, 7) | AB = 1

X3293 (SS(a → b + c) OF X3) 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 \(f(a,b,c) = (b + c)[(c + a)^{2} + (a + b)^{2} - (b + c)^{2}]\)
Barycentrics: \(af(a,b,c) : bf(b,c,a) : cf(c,a,b)\)
Search Value (6, 9, 13): \(0.547812289893\)
▸ Incident Central Lines12 lines

{1, 2}, {37, 762}, {40, 209}, {55, 1724}, {58, 100}, {71, 380}, {81, 1126}, {191, 1045}, {213, 1018}, {484, 1046}, {740, 872}, {942, 1739}

▸ Functional Relations2 relations