X3974

X2999com(EXCENTRAL TRIANGLE)

< 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) { 8, 210 }: Central Line L(8, 210) { 33, 200 }: Central Line L(33, 200) { 55, 346 }: Central Line L(55, 346) { 4, 1089 }: Central Line L(4, 1089) { 2, 1390 }: Central Line L(2, 1390) { 756, 966 }: Central Line L(756, 966) A = Vertex A (0.0000, 0.0000) B = Vertex B (1.0000, 0.0000) C = Vertex C (0.6122, 0.5999) X_8 = NAGEL POINT (0.4694, 0.1333) X_210 = -CEVA CONJUGATE OF X(37) (0.4925, 0.1466) X_33 = PERSPECTOR OF THE ORTHIC AND INTANGENTS TRIANGLES (0.6019, 0.3546) X_200 = -CEVA CONJUGATE OF X(9) (0.4392, 0.1037) X_55 = INSIMILICENTER(CIRCUMCIRCLE, INCIRCLE) (0.5490, 0.1921) X_346 = ISOTOMIC CONJUGATE OF X(279) (0.3948, 0.0827) X_4 = ORTHOCENTER (0.6122, 0.3958) X_1089 = TRILINEAR SQUARE OF X(10) (0.4606, 0.1381) X_2 = CENTROID (0.5374, 0.2000) X_1390 = ISOGONAL CONJUGATE OF X(1386) (0.5559, 0.2165) X_756 = CROSSPOINT OF X(10) AND X(37) (0.5409, 0.1988) X_966 = INTERSECTION OF LINES X(2)X(6) AND X(4)X(9) (0.5191, 0.1803) X_3974 = com(EXCENTRAL TRIANGLE) (0.4518, 0.1232) A B C X8 X210 X33 X200 X55 X346 X4 X1089 X2 X1390 X756 X966 X3974 (a, b, c) = (5, 6, 7) | AB = 1

X3974 (X2999com(EXCENTRAL TRIANGLE)) constructed on acute reference triangle \((a, b, c) = (5, 6, 7)\) with unit baseline AB = \(1\).

Constructed Elements

Barycentrics: \(f(a,b,c) : f(b,c,a) : f(c,a,b)\), where \(f(a,b,c) = (b + c - a)(a^{2} + b^{2} + c^{2} + 2bc)\)
Search Value (6, 9, 13): \(4.851348688684\)
▸ Incident Central Lines15 lines

{2, 1390}, {4, 1089}, {8, 210}, {33, 200}, {55, 346}, {321, 2550}, {329, 3416}, {344, 3757}, {391, 3715}, {612, 2345}, {756, 966}, {1219, 3304}, {3085, 3695}, {3161, 3683}, {3474, 3729}