X3840

X3210com(3rd EULER TRIANGLE)

X3840 = complement of X43
< 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, 43 }: Nagel Line { 1, 2 }: Nagel Line { 244, 321 }: Central Line L(244, 321) { 312, 726 }: Central Line L(312, 726) { 354, 1215 }: Central Line L(354, 1215) 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_43 = -CEVA CONJUGATE OF X(1) (0.6358, 0.2963) X_1 = INCENTER (0.5714, 0.2333) X_244 = -LINE CONJUGATE OF X(100) (0.7857, 0.1166) X_321 = ISOTOMIC CONJUGATE OF X(81) (0.4800, 0.1527) X_312 = ISOTOMIC CONJUGATE OF X(57) (0.4256, 0.1081) X_726 = EVEN (- 2, -1) INFINITY POINT (1.0187, 0.5358) X_354 = WEILL POINT (0.5823, 0.2533) X_1215 = ISOGONAL CONJUGATE OF X(1178) (0.5340, 0.2011) X_3840 = com(3rd EULER TRIANGLE) (0.4882, 0.1518) A B C Ma Mb Mc X2 X43 X1 X244 X321 X312 X726 X354 X1215 X3840 (a, b, c) = (5, 6, 7) | AB = 1

X3840 (X3210com(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 \(f(a,b,c) = ab^{2} + ac^{2} + b^{2}c + bc^{2} - 2abc\)
Search Value (6, 9, 13): \(3.815442758666\)
▸ Incident Central Lines12 lines

{1, 2}, {11, 2887}, {226, 1401}, {244, 321}, {312, 726}, {350, 3663}, {354, 1215}, {740, 3752}, {748, 1150}, {1575, 2321}, {2810, 3038}, {3551, 3662}

▸ Functional Relations4 relations