X1708

MIMOSA TRANSFORM OF X7

X1708 = X273-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) { 2, 7 }: Centroid–Gergonne Line { 4, 46 }: Central Line L(4, 46) { 56, 72 }: Central Line L(56, 72) { 1, 201 }: Central Line L(1, 201) { 218, 222 }: Central Line L(218, 222) { 65, 405 }: Central Line L(65, 405) A = Vertex A (0.0000, 0.0000) B = Vertex B (1.0000, 0.0000) C = Vertex C (0.6122, 0.5999) X_273 = ISOGONAL CONJUGATE OF X(212) (0.6191, 0.4329) X_1 = INCENTER (0.5714, 0.2333) X_2 = CENTROID (0.5374, 0.2000) X_7 = GERGONNE POINT (0.5903, 0.2769) X_4 = ORTHOCENTER (0.6122, 0.3958) X_46 = -CEVA CONJUGATE OF X(1) (0.6917, 0.4543) X_56 = EXSIMILICENTER(CIRCUMCIRCLE, INCIRCLE) (0.6316, 0.3438) X_72 = ISOGONAL CONJUGATE OF X(28) (0.4367, 0.0733) X_201 = -CEVA CONJUGATE OF X(12) (0.4897, 0.1062) X_218 = -CEVA CONJUGATE OF X(55) (0.6557, 0.3333) X_222 = -CEVA CONJUGATE OF X(56) (0.5653, 0.1568) X_65 = ORTHOCENTER OF THE INTOUCH TRIANGLE (0.6041, 0.2933) X_405 = EULER LINE INTERCEPT OF LINE X(1)X(6) (0.5325, 0.1870) X_1708 = MIMOSA TRANSFORM OF X(7) (0.7332, 0.4848) A B C X273 X1 X2 X7 X4 X46 X56 X72 X201 X218 X222 X65 X405 X1708 (a, b, c) = (5, 6, 7) | AB = 1

X1708 (MIMOSA TRANSFORM OF X7) 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 \(f(a,b,c) = - (\cos A)/x + (\cos B)/y + (\cos C)/z\),\(x : y : z\) = X7
Barycentrics: \(af(a,b,c) : bf(b,c,a) : cf(c,a,b)\)
Search Value (6, 9, 13): \(-0.650040859100\)
▸ Incident Central Lines33 lines

{1, 201}, {2, 7}, {4, 46}, {6, 1214}, {19, 1713}, {33, 1736}, {34, 1724}, {38, 1471}, {40, 950}, {43, 1758}, {44, 1427}, {56, 72}, {58, 1038}, {65, 405}, {109, 1395}, {169, 1762}, {208, 860}, {218, 222}, {223, 1743}, {225, 1714}, {278, 1723}, {354, 954}, {442, 1454}, {518, 1260}, {582, 1062}, {653, 1748}, {1020, 1435}, {115, 1864}, {1396, 1778}, {1412, 1812}, {1711, 1738}, {1712, 1715}, {1750, 1768}

▸ Functional Relations5 relations