X1759

MIMOSA TRANSFORM OF X304

X1759 = X76-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, 32 }: Central Line L(1, 32) { 9, 46 }: Central Line L(9, 46) { 63, 169 }: Central Line L(63, 169) { 40, 728 }: Central Line L(40, 728) { 41, 758 }: Central Line L(41, 758) { 72, 910 }: Central Line L(72, 910) A = Vertex A (0.0000, 0.0000) B = Vertex B (1.0000, 0.0000) C = Vertex C (0.6122, 0.5999) X_76 = 3rd BROCARD POINT (0.4567, 0.1388) X_1 = INCENTER (0.5714, 0.2333) X_32 = 3rd POWER POINT (0.6400, 0.3332) X_9 = MITTENPUNKT (0.5110, 0.1615) X_46 = -CEVA CONJUGATE OF X(1) (0.6917, 0.4543) X_63 = ISOGONAL CONJUGATE OF X(19) (0.4566, 0.0823) X_169 = -CEVA CONJUGATE OF X(1) (0.5497, 0.2510) X_40 = BEVAN POINT (0.4286, -0.0292) X_728 = INTERSECTION OF LINES X(8)X(9) AND X(57)X(345) (0.3648, 0.0624) X_41 = -CEVA CONJUGATE OF X(31) (0.5823, 0.2244) X_758 = EVEN (1, 3) INFINITY POINT (0.1821, -0.2671) X_72 = ISOGONAL CONJUGATE OF X(28) (0.4367, 0.0733) X_910 = CROSSPOINT OF X(57) AND X(105) (1.3163, 2.5495) X_1759 = MIMOSA TRANSFORM OF X(304) (0.4099, -0.0023) A B C X76 X1 X32 X9 X46 X63 X169 X40 X728 X41 X758 X72 X910 X1759 (a, b, c) = (5, 6, 7) | AB = 1

X1759 (MIMOSA TRANSFORM OF X304) 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 \(f(a,b,c) = a^{3} - b^{3} - c^{3}\) (M. Iliev, 5/13/07)
Barycentrics: \(af(a,b,c) : bf(b,c,a) : cf(c,a,b)\)
Search Value (6, 9, 13): \(8.471638685443\)
▸ Incident Central Lines6 lines

{1, 32}, {9, 46}, {40, 728}, {41, 758}, {63, 169}, {72, 910}

▸ Functional Relations3 relations