X1707

MIMOSA TRANSFORM OF X6

X1707 = isogonal conjugate of X8769
< 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, 21 }: Central Line L(1, 21) { 9, 171 }: Central Line L(9, 171) { 43, 165 }: Central Line L(43, 165) { 57, 238 }: Central Line L(57, 238) { 204, 240 }: Central Line L(204, 240) { 326, 560 }: Central Line L(326, 560) A = Vertex A (0.0000, 0.0000) B = Vertex B (1.0000, 0.0000) C = Vertex C (0.6122, 0.5999) X_1 = INCENTER (0.5714, 0.2333) X_21 = SCHIFFLER POINT (0.5287, 0.1771) X_9 = MITTENPUNKT (0.5110, 0.1615) X_171 = {X(2), X(31)}-HARMONIC CONJUGATE OF X(238) (0.5819, 0.2525) X_43 = -CEVA CONJUGATE OF X(1) (0.6358, 0.2963) X_165 = CENTROID OF THE EXCENTRAL TRIANGLE (0.4762, 0.0583) X_57 = ISOGONAL CONJUGATE OF X(9) (0.6138, 0.3110) X_238 = -LINE CONJUGATE OF X(37) (1.6190, 1.4775) X_204 = -CEVA CONJUGATE OF X(19) (0.6683, 3.3982) X_240 = -LINE CONJUGATE OF X(48) (0.7457, 0.8594) X_326 = ISOTOMIC CONJUGATE OF X(158) (0.3354, 0.0219) X_560 = 4th POWER POINT (0.6520, 0.3639) X_1707 = MIMOSA TRANSFORM OF X(6) (0.7574, 0.4777) A B C X1 X21 X9 X171 X43 X165 X57 X238 X204 X240 X326 X560 X1707 (a, b, c) = (5, 6, 7) | AB = 1

X1707 (MIMOSA TRANSFORM OF X6) 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 \(f(a,b,c) = - (\cos A)/x + (\cos B)/y + (\cos C)/z\),\(x : y : z\) = X6
Barycentrics: \(af(a,b,c) : bf(b,c,a) : cf(c,a,b)\)
Search Value (6, 9, 13): \(-1.473830402106\)
▸ Alternate Coordinates3 forms

  • Trilinears: \(3a^{2} - b^{2} - c^{2} : 3b^{2} - c^{2} - a^{2} : 3c^{2} - a^{2} - b^{2}\) (M. Iliev, 5/13/2007)

  • Trilinears: \(\cot B + \cot C - \cot A : \cot C + \cot A - \cot B : \cot A + \cot B - \cot C\) (Randy Hutson, 9/23/2011)

  • Trilinears: \(a^{2} - S_{A} : b^{2} - S_{B} : c^{2} - S_{C}\) (C. Lozada, 9/07/2013)

▸ Incident Central Lines29 lines

{1, 21}, {9, 171}, {19, 1719}, {33, 1776}, {36, 1473}, {43, 165}, {44, 1376}, {46, 1722}, {57, 238}, {92, 1733}, {109, 1395}, {162, 1096}, {200, 1757}, {204, 240}, {223, 1758}, {326, 560}, {380, 1045}, {484, 1774}, {579, 1716}, {580, 1158}, {610, 1740}, {978, 1044}, {986, 1453}, {1038, 1399}, {1633, 1732}, {1709, 1711}, {1714, 1770}, {1728, 1771}, {1788, 1877}

▸ Functional Relations5 relations