X3214

X57-CEVA CONJUGATE OF X37

X3214 = reflection of X1201 in X3216
< 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) { 1201, 3216 }: Nagel Line { 1, 2 }: Nagel Line { 44, 71 }: Central Line L(44, 71) { 65, 2137 }: Central Line L(65, 2137) { 210, 2292 }: Central Line L(210, 2292) A = Vertex A (0.0000, 0.0000) B = Vertex B (1.0000, 0.0000) C = Vertex C (0.6122, 0.5999) X_1201 = 3rd SARAGOSSA POINT OF X(56) (0.6184, 0.2793) X_3216 = -CEVA CONJUGATE OF X(1) (0.6654, 0.3254) X_1 = INCENTER (0.5714, 0.2333) X_2 = CENTROID (0.5374, 0.2000) X_44 = -LINE CONJUGATE OF X(1) (2.1429, 2.0996) X_71 = ISOGONAL CONJUGATE OF X(27) (0.4807, 0.0915) X_65 = ORTHOCENTER OF THE INTOUCH TRIANGLE (0.6041, 0.2933) X_2137 = ISOGONAL CONJUGATE OF X(2136) (-4.1633, -1.4664) X_210 = -CEVA CONJUGATE OF X(37) (0.4925, 0.1466) X_2292 = -ISOCONJUGATE OF X(1169) (0.5509, 0.2064) X_3214 = -CEVA CONJUGATE OF X(37) (0.7124, 0.3714) A B C X1201 X3216 X1 X2 X44 X71 X65 X2137 X210 X2292 X3214 (a, b, c) = (5, 6, 7) | AB = 1

X3214 (X57-CEVA CONJUGATE OF X37) 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 \(f(a,b,c) = (b + c)(a^{2} + ab + ac - 2bc)\) (M. Iliev, 5/13/07)
Barycentrics: \(af(a,b,c) : bf(b,c,a) : cf(c,a,b)\)
Search Value (6, 9, 13): \(-1.192579181599\)
▸ Incident Central Lines13 lines

{1, 2}, {44, 71}, {65, 2137}, {209, 2390}, {210, 2292}, {405, 2177}, {902, 1724}, {1334, 2238}, {1376, 1468}, {1458, 1788}, {1475, 1575}, {1834, 2318}, {2246, 2333}

▸ Functional Relations2 relations