X3815

X574com(5th EULER TRIANGLE)

X3815 = crosspoint of X2 and X262
< 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) { 2, 6 }: Centroid–Symmedian Line { 5, 39 }: Central Line L(5, 39) { 32, 140 }: Central Line L(32, 140) { 25, 160 }: Central Line L(25, 160) { 53, 232 }: Central Line L(53, 232) { 30, 574 }: Central Line L(30, 574) A = Vertex A (0.0000, 0.0000) B = Vertex B (1.0000, 0.0000) C = Vertex C (0.6122, 0.5999) X_2 = CENTROID (0.5374, 0.2000) X_262 = ISOGONAL CONJUGATE OF X(182) (0.5893, 0.2856) X_6 = SYMMEDIAN POINT (LEMOINE POINT, GREBE POINT) (0.6000, 0.2672) X_5 = NINE-POINT CENTER (0.5561, 0.2489) X_39 = BROCARD MIDPOINT (0.5778, 0.2305) X_32 = 3rd POWER POINT (0.6400, 0.3332) X_140 = MIDPOINT OF X(3) AND X(5) (0.5281, 0.1755) X_25 = HOMOTHETIC CENTER OF ORTHIC AND TANGENTIAL TRIANGLES (0.6329, 0.4497) X_160 = -OF-TANGENTIAL-TRIANGLE (0.4841, -0.0647) X_53 = SYMMEDIAN POINT OF ORTHIC TRIANGLE (0.6164, 0.4390) X_232 = -CEVA CONJUGATE OF X(132) (0.6919, 0.7779) X_30 = EULER INFINITY POINT (0.7469, 0.7481) X_574 = HARMONIC OF X(187) (0.5539, 0.1910) X_3815 = com(5th EULER TRIANGLE) (0.5711, 0.2362) A B C X2 X262 X6 X5 X39 X32 X140 X25 X160 X53 X232 X30 X574 X3815 (a, b, c) = (5, 6, 7) | AB = 1

X3815 (X574com(5th 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 \(f(a,b,c) = b^{4} + c^{4} - 3a^{2}b^{2} - 3a^{2}c^{2} - 2b^{2}c^{2}\)
Search Value (6, 9, 13): \(1.397671761976\)
▸ Incident Central Lines26 lines

{2, 6}, {3, 2548}, {5, 39}, {11, 2276}, {12, 2275}, {25, 160}, {30, 574}, {32, 140}, {53, 232}, {187, 549}, {216, 1368}, {233, 1196}, {251, 2965}, {262, 1513}, {381, 2549}, {495, 1015}, {496, 1500}, {543, 3363}, {566, 858}, {594, 3705}, {631, 1285}, {1107, 1329}, {1575, 2886}, {1595, 3199}, {2207, 3541}, {2963, 3108}

▸ Functional Relations6 relations