X1716

MIMOSA TRANSFORM OF X31

X1716 = X25-Ceva conjugate of X1
< 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) { 9, 43 }: Central Line L(9, 43) { 1, 69 }: Central Line L(1, 69) { 3, 238 }: Central Line L(3, 238) { 579, 1707 }: Central Line L(579, 1707) { 1402, 1423 }: Central Line L(1402, 1423) { 4, 1721 }: Central Line L(4, 1721) A = Vertex A (0.0000, 0.0000) B = Vertex B (1.0000, 0.0000) C = Vertex C (0.6122, 0.5999) X_25 = HOMOTHETIC CENTER OF ORTHIC AND TANGENTIAL TRIANGLES (0.6329, 0.4497) X_1 = INCENTER (0.5714, 0.2333) X_9 = MITTENPUNKT (0.5110, 0.1615) X_43 = -CEVA CONJUGATE OF X(1) (0.6358, 0.2963) X_69 = SYMMEDIAN POINT OF THE ANTICOMPLEMENTARY TRIANGLE (0.4122, 0.0654) X_3 = CIRCUMCENTER (0.5000, 0.1021) X_238 = -LINE CONJUGATE OF X(37) (1.6190, 1.4775) X_579 = HARMONIC OF X(284) (0.7212, 0.4674) X_1707 = MIMOSA TRANSFORM OF X(6) (0.7574, 0.4777) X_1402 = -BETH CONJUGATE OF X(42) (0.6396, 0.3585) X_1423 = -BETH CONJUGATE OF X(192) (0.6537, 0.3692) X_4 = ORTHOCENTER (0.6122, 0.3958) X_1721 = MIMOSA TRANSFORM OF X(55) (0.6494, 0.4136) X_1716 = MIMOSA TRANSFORM OF X(31) (0.8201, 0.4954) A B C X25 X1 X9 X43 X69 X3 X238 X579 X1707 X1402 X1423 X4 X1721 X1716 (a, b, c) = (5, 6, 7) | AB = 1

X1716 (MIMOSA TRANSFORM OF X31) 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 \(f(a,b,c) = - (\cos A)/x + (\cos B)/y + (\cos C)/z\),\(x : y : z\) = X31
Barycentrics: \(af(a,b,c) : bf(b,c,a) : cf(c,a,b)\)
Search Value (6, 9, 13): \(-1.749297702363\)
▸ Incident Central Lines7 lines

{1, 69}, {3, 238}, {4, 1721}, {9, 43}, {579, 1707}, {1402, 1423}, {1745, 1756}

▸ Functional Relations2 relations