X1758

MIMOSA TRANSFORM OF X296

X1758 = crossdifference of PU(80)
< 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, 3 }: OI Line (Incenter–Circumcenter Line) { 108, 240 }: Central Line L(108, 240) { 226, 846 }: Central Line L(226, 846) { 73, 1046 }: Central Line L(73, 1046) { 411, 774 }: Central Line L(411, 774) { 21, 1254 }: Central Line L(21, 1254) A = Vertex A (0.0000, 0.0000) B = Vertex B (1.0000, 0.0000) C = Vertex C (0.6122, 0.5999) X_1937 = TRILINEAR POLE OF PU(15) (0.8541, -0.3793) X_1 = INCENTER (0.5714, 0.2333) X_3 = CIRCUMCENTER (0.5000, 0.1021) X_108 = Ψ(CIRCUMCENTER, INCENTER) (0.5320, 0.6114) X_240 = -LINE CONJUGATE OF X(48) (0.7457, 0.8594) X_226 = -CEVA CONJUGATE OF X(65) (0.5778, 0.2588) X_846 = 4th SHARYGIN POINT (0.5437, 0.1969) X_73 = CROSSPOINT OF INCENTER AND CIRCUMCENTER (0.5487, 0.1428) X_1046 = -CEVA CONJUGATE OF X(1) (0.6500, 0.3366) X_411 = EULER X(21)-2nd-SUBSTITUTION POINT (0.4414, -0.0514) X_774 = CROSSPOINT OF X(1) AND X(158) (0.6363, 0.3186) X_21 = SCHIFFLER POINT (0.5287, 0.1771) X_1254 = ISOGONAL CONJUGATE OF X(1098) (0.6258, 0.3523) X_1758 = MIMOSA TRANSFORM OF X(296) (1.1982, 1.3847) A B C X1937 X1 X3 X108 X240 X226 X846 X73 X1046 X411 X774 X21 X1254 X1758 (a, b, c) = (5, 6, 7) | AB = 1

X1758 (MIMOSA TRANSFORM OF X296) 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 \(f(a,b,c) = - (\cos A)/x + (\cos B)/y + (\cos C)/z\),\(x : y : z\) = X296
Barycentrics: \(af(a,b,c) : bf(b,c,a) : cf(c,a,b)\)
Search Value (6, 9, 13): \(-1.039344872577\)
▸ Alternate Coordinates1 form

  • Trilinears: \((a^{3} + b^{3} + c^{3} - 2a^{2}b - 2a^{2}c + abc)/(b + c - a) : :\)

▸ Incident Central Lines14 lines

{1, 3}, {21, 1254}, {43, 1708}, {73, 1046}, {108, 240}, {223, 1707}, {225, 1247}, {226, 846}, {238, 1465}, {411, 774}, {651, 896}, {920, 1745}, {1044, 1158}, {1054, 1738}

▸ Functional Relations5 relations