X976

INTERSECTION OF LINES X1X_2 AND X3X_38

X976 = isogonal conjugate of X977
< 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) { 1, 2 }: Nagel Line { 3, 38 }: Central Line L(3, 38) { 37, 41 }: Central Line L(37, 41) { 31, 72 }: Central Line L(31, 72) { 66, 73 }: Central Line L(66, 73) { 244, 474 }: Central Line L(244, 474) A = Vertex A (0.0000, 0.0000) B = Vertex B (1.0000, 0.0000) C = Vertex C (0.6122, 0.5999) X_977 = ISOGONAL CONJUGATE OF X(976) (0.5890, 0.2525) X_1 = INCENTER (0.5714, 0.2333) X_2 = CENTROID (0.5374, 0.2000) X_3 = CIRCUMCENTER (0.5000, 0.1021) X_38 = CROSSPOINT OF X(1) AND X(75) (0.5443, 0.1976) X_37 = CROSSPOINT OF INCENTER AND CENTROID (0.5567, 0.2158) X_41 = -CEVA CONJUGATE OF X(31) (0.5823, 0.2244) X_31 = 2nd POWER POINT (0.6228, 0.3008) X_72 = ISOGONAL CONJUGATE OF X(28) (0.4367, 0.0733) X_66 = ISOGONAL CONJUGATE OF X(22) (0.5912, 1.0593) X_73 = CROSSPOINT OF INCENTER AND CIRCUMCENTER (0.5487, 0.1428) X_244 = -LINE CONJUGATE OF X(100) (0.7857, 0.1166) X_474 = EULER LINE INTERCEPT OF LINE X(10)X(56) (0.5441, 0.2176) X_976 = INTERSECTION OF LINES X(1)X(2) AND X(3)X(38) (0.5520, 0.2143) A B C X977 X1 X2 X3 X38 X37 X41 X31 X72 X66 X73 X244 X474 X976 (a, b, c) = (5, 6, 7) | AB = 1

X976 (INTERSECTION OF LINES X1X_2 AND X3X_38) constructed on acute reference triangle \((a, b, c) = (5, 6, 7)\) with unit baseline AB = \(1\).

Constructed Elements

Trilinears: \(f(a,b,c) : f(b,c,a) : f(c,a,b)\), where \(f(a,b,c) = a^{3} + (b + c)(b^{2} + c^{2})\)
Barycentrics: \(g(a,b,c) : g(b,c,a) : g(c,a,b)\), where \(g(a,b,c) = af(a,b,c)\)
Search Value (6, 9, 13): \(2.125341715807\)
▸ Incident Central Lines14 lines

{1, 2}, {3, 38}, {21, 983}, {31, 72}, {37, 41}, {66, 73}, {100, 986}, {210, 1104}, {244, 474}, {404, 982}, {405, 756}, {601, 912}, {750, 942}, {1060, 1066}

▸ Functional Relations1 relation