X1745

MIMOSA TRANSFORM OF X255

X1745 = X1148-cross 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 { 43, 46 }: Central Line L(43, 46) { 255, 411 }: Central Line L(255, 411) { 36, 978 }: Central Line L(36, 978) { 579, 610 }: Central Line L(579, 610) { 78, 1330 }: Central Line L(78, 1330) 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_4 = ORTHOCENTER (0.6122, 0.3958) X_43 = -CEVA CONJUGATE OF X(1) (0.6358, 0.2963) X_46 = -CEVA CONJUGATE OF X(1) (0.6917, 0.4543) X_255 = ISOGONAL CONJUGATE OF X(158) (0.4217, 0.0365) X_411 = EULER X(21)-2nd-SUBSTITUTION POINT (0.4414, -0.0514) X_36 = INVERSE-IN-CIRCUMCIRCLE OF INCENTER (1.3333, 1.6330) X_978 = -CEVA CONJUGATE OF X(1) (0.7456, 0.4040) X_579 = HARMONIC OF X(284) (0.7212, 0.4674) X_610 = -CEVA CONJUGATE OF X(1) (0.4310, -0.2713) X_78 = ISOGONAL CONJUGATE OF X(34) (0.3835, 0.0491) X_1330 = ANTICOMPLEMENTARY CONJUGATE OF X(1) (0.3908, 0.0300) X_1745 = MIMOSA TRANSFORM OF X(255) (0.4689, -0.1747) A B C X1 X4 X43 X46 X255 X411 X36 X978 X579 X610 X78 X1330 X1745 (a, b, c) = (5, 6, 7) | AB = 1

X1745 (MIMOSA TRANSFORM OF X255) 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 \(f(A,B,C) = \sec B + \sec C - \sec A\) (D. Grinberg, 2/25/04)
Barycentrics: \(af(a,b,c) : bf(b,c,a) : cf(c,a,b)\)
Search Value (6, 9, 13): \(-3.491508980194\)

X1745 lies on the McCay cubic.

▸ Incident Central Lines11 lines

{1, 4}, {35, 1742}, {36, 978}, {43, 46}, {78, 1330}, {255, 411}, {579, 610}, {908, 1076}, {920, 1758}, {1464, 1836}, {1716, 1756}

▸ Functional Relations7 relations