X3848

X553com(3rd EULER TRIANGLE)

X3848 = complement of X3740
< A B C >: Reference Triangle △ABC < M_a M_b M_c >: Medial Triangle △M_a M_b M_c [ A B ]: Sideline AB (Base c = 1) [ B C ]: Sideline BC (Side a) [ C A ]: Sideline CA (Side b) { 2, 3740 }: Central Line L(2, 3740) { 2, 210 }: Central Line L(2, 210) { 140, 517 }: Central Line L(140, 517) { 165, 1001 }: Central Line L(165, 1001) { 142, 1538 }: Central Line L(142, 1538) A = Vertex A (0.0000, 0.0000) B = Vertex B (1.0000, 0.0000) C = Vertex C (0.6122, 0.5999) M_a = Midpoint M_a of BC (0.8061, 0.2999) M_b = Midpoint M_b of CA (0.3061, 0.2999) M_c = Midpoint M_c of AB (0.5000, 0.0000) X_2 = CENTROID (0.5374, 0.2000) X_3740 = com[n(INCENTRAL)*n(MEDIAL)] (0.5150, 0.1733) X_210 = -CEVA CONJUGATE OF X(37) (0.4925, 0.1466) X_140 = MIDPOINT OF X(3) AND X(5) (0.5281, 0.1755) X_517 = ISOGONAL CONJUGATE OF X(104) (0.8180, 0.7154) X_165 = CENTROID OF THE EXCENTRAL TRIANGLE (0.4762, 0.0583) X_1001 = MIDPOINT OF X(1) AND X(9) (0.5412, 0.1974) X_142 = COMPLEMENT OF X(9) (0.5506, 0.2192) X_1538 = ORTHOJOIN OF X(45) (1.0204, 1.6122) X_3848 = com(3rd EULER TRIANGLE) (0.5486, 0.2133) A B C Ma Mb Mc X2 X3740 X210 X140 X517 X165 X1001 X142 X1538 X3848 (a, b, c) = (5, 6, 7) | AB = 1

X3848 (X553com(3rd EULER 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 \(f(a,b,c) = a(b^{2} + c^{2} - ab - ac - 8bc)\)
Search Value (6, 9, 13): \(2.297888538735\)
▸ Incident Central Lines8 lines

{2, 210}, {140, 517}, {142, 1538}, {165, 1001}, {171, 3246}, {960, 3624}, {3149, 3576}, {3622, 3698}

▸ Functional Relations1 relation