X3827

X518com(2nd EULER TRIANGLE)

X3827 = crossdifference of every pair of points on line X6X521
< 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) { 6, 19 }: Central Line L(6, 19) { 66, 72 }: Central Line L(66, 72) { 1, 159 }: Central Line L(1, 159) { 154, 354 }: Central Line L(154, 354) { 30, 511 }: Central Line L(30, 511) { 141, 960 }: Central Line L(141, 960) A = Vertex A (0.0000, 0.0000) B = Vertex B (1.0000, 0.0000) C = Vertex C (0.6122, 0.5999) X_6 = SYMMEDIAN POINT (LEMOINE POINT, GREBE POINT) (0.6000, 0.2672) X_19 = CLAWSON POINT (0.6246, 0.4244) X_66 = ISOGONAL CONJUGATE OF X(22) (0.5912, 1.0593) X_72 = ISOGONAL CONJUGATE OF X(28) (0.4367, 0.0733) X_1 = INCENTER (0.5714, 0.2333) X_159 = -OF-TANGENTIAL-TRIANGLE (0.4211, -0.7266) X_154 = -CEVA CONJUGATE OF X(6) (0.4807, -0.3954) X_354 = WEILL POINT (0.5823, 0.2533) X_30 = EULER INFINITY POINT (0.7469, 0.7481) X_511 = ISOGONAL CONJUGATE OF X(98) (0.2335, -0.3020) X_141 = COMPLEMENT OF SYMMEDIAN POINT (0.5061, 0.1663) X_960 = INTERSECTION OF LINES X(1)X(6) AND X(5)X(10) (0.5041, 0.1533) X_3827 = com(2nd EULER TRIANGLE) (0.4466, -0.3798) A B C X6 X19 X66 X72 X1 X159 X154 X354 X30 X511 X141 X960 X3827 (a, b, c) = (5, 6, 7) | AB = 1

X3827 (X518com(2nd 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 \(f(a,b,c) = a(b^{5} + c^{5} - a^{4}b - a^{4}c - b^{4}c - bc^{4} + 2a^{3}bc)\)
▸ Incident Central Lines16 lines

{1, 159}, {6, 19}, {30, 511}, {66, 72}, {141, 960}, {154, 354}, {197, 1763}, {206, 942}, {210, 1853}, {1214, 3185}, {1279, 2195}, {1633, 3100}, {1824, 1836}, {1828, 1837}, {1843, 1858}, {1854, 3057}

▸ Functional Relations1 relation

  • X3827 = crossdifference of every pair of points on line X6X521