X1740

MIMOSA TRANSFORM OF X184

X1740 = X1613-cross conjugate of X1424
< 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) { 6, 43 }: Central Line L(6, 43) { 1, 75 }: Central Line L(1, 75) { 3, 238 }: Central Line L(3, 238) { 560, 662 }: Central Line L(560, 662) { 19, 1581 }: Central Line L(19, 1581) { 31, 1582 }: Central Line L(31, 1582) A = Vertex A (0.0000, 0.0000) B = Vertex B (1.0000, 0.0000) C = Vertex C (0.6122, 0.5999) X_6 = SYMMEDIAN POINT (LEMOINE POINT, GREBE POINT) (0.6000, 0.2672) X_43 = -CEVA CONJUGATE OF X(1) (0.6358, 0.2963) X_1 = INCENTER (0.5714, 0.2333) X_75 = ISOTOMIC CONJUGATE OF INCENTER (0.4988, 0.1682) X_3 = CIRCUMCENTER (0.5000, 0.1021) X_238 = -LINE CONJUGATE OF X(37) (1.6190, 1.4775) X_560 = 4th POWER POINT (0.6520, 0.3639) X_662 = TRILINEAR POLE OF LINE X(1)X(21) (0.1811, 0.4951) X_19 = CLAWSON POINT (0.6246, 0.4244) X_1581 = ISOGONAL CONJUGATE OF X(1580) (1.0304, 0.0330) X_31 = 2nd POWER POINT (0.6228, 0.3008) X_1582 = POINT CANOPUS (0.5834, 0.2762) X_1740 = MIMOSA TRANSFORM OF X(184) (0.7017, 0.3500) A B C X6 X43 X1 X75 X3 X238 X560 X662 X19 X1581 X31 X1582 X1740 (a, b, c) = (5, 6, 7) | AB = 1

X1740 (MIMOSA TRANSFORM OF X184) 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 \(f(a,b,c) = a^{2}b^{2} + a^{2}c^{2} - b^{2}c^{2}\) (M. Iliev, 5/13/07)
Barycentrics: \(af(a,b,c) : bf(b,c,a) : cf(c,a,b)\)
Search Value (6, 9, 13): \(-0.776783661037\)
▸ Incident Central Lines9 lines

{1, 75}, {3, 238}, {6, 43}, {19, 1581}, {31, 1582}, {48, 1580}, {560, 662}, {610, 1707}, {869, 894}

▸ Functional Relations6 relations