X1750

MIMOSA TRANSFORM OF X268

X1750 = X282-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) { 1, 4 }: Incenter–Orthocenter Line { 9, 165 }: Central Line L(9, 165) { 40, 210 }: Central Line L(40, 210) { 200, 329 }: Central Line L(200, 329) { 20, 936 }: Central Line L(20, 936) { 57, 971 }: Central Line L(57, 971) A = Vertex A (0.0000, 0.0000) B = Vertex B (1.0000, 0.0000) C = Vertex C (0.6122, 0.5999) X_282 = -CROSS CONJUGATE OF X(9) (0.6199, 0.7507) X_1 = INCENTER (0.5714, 0.2333) X_4 = ORTHOCENTER (0.6122, 0.3958) X_9 = MITTENPUNKT (0.5110, 0.1615) X_165 = CENTROID OF THE EXCENTRAL TRIANGLE (0.4762, 0.0583) X_40 = BEVAN POINT (0.4286, -0.0292) X_210 = -CEVA CONJUGATE OF X(37) (0.4925, 0.1466) X_200 = -CEVA CONJUGATE OF X(9) (0.4392, 0.1037) X_329 = ISOTOMIC CONJUGATE OF X(189) (0.3847, -0.0222) X_20 = DE LONGCHAMPS POINT (0.3878, -0.1916) X_936 = INTERSECTION OF LINES X(1)X(2) AND X(3)X(9) (0.5138, 0.1768) X_57 = ISOGONAL CONJUGATE OF X(9) (0.6138, 0.3110) X_971 = INTERSECTION OF LINES X(3)X(9) AND X(4)X(7) (0.6441, 0.7770) X_1750 = MIMOSA TRANSFORM OF X(268) (0.6772, 0.6545) A B C X282 X1 X4 X9 X165 X40 X210 X200 X329 X20 X936 X57 X971 X1750 (a, b, c) = (5, 6, 7) | AB = 1

X1750 (MIMOSA TRANSFORM OF X268) 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 \(f(a,b,c) = - (\cos A)/x + (\cos B)/y + (\cos C)/z\),\(x : y : z\) = X268
Search Value (6, 9, 13): \(-14.938577021441\)
▸ Alternate Coordinates1 form

  • Trilinears: \((1 + \cos A - \cos B - \cos C) (\tan A/2) - (1 + \cos B - \cos C - \cos A) (\tan B/2) - (1 + \cos C - \cos A - \cos B) (\tan C/2) : :\)

▸ Incident Central Lines10 lines

{1, 4}, {9, 165}, {20, 936}, {40, 210}, {43, 1721}, {57, 971}, {84, 1728}, {200, 329}, {1708, 1768}, {1743, 1754}

▸ Functional Relations2 relations