X1779

MIMOSA TRANSFORM OF X1172

< 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) { 4, 46 }: Central Line L(4, 46) { 35, 47 }: Central Line L(35, 47) { 43, 165 }: Central Line L(43, 165) { 378, 580 }: Central Line L(378, 580) { 579, 1172 }: Central Line L(579, 1172) { 1714, 1715 }: Central Line L(1714, 1715) A = Vertex A (0.0000, 0.0000) B = Vertex B (1.0000, 0.0000) C = Vertex C (0.6122, 0.5999) X_4 = ORTHOCENTER (0.6122, 0.3958) X_46 = -CEVA CONJUGATE OF X(1) (0.6917, 0.4543) X_35 = {X(1),X(3)}-HARMONIC CONJUGATE OF X(36) (0.5373, 0.1706) X_47 = -BETH CONJUGATE OF X(34) (0.7279, 0.4389) X_43 = -CEVA CONJUGATE OF X(1) (0.6358, 0.2963) X_165 = CENTROID OF THE EXCENTRAL TRIANGLE (0.4762, 0.0583) X_378 = REFLECTION OF X(22) IN X(3) (0.5857, 0.3262) X_580 = ORTHOGONAL OF X(284) (0.7089, 0.4470) X_579 = HARMONIC OF X(284) (0.7212, 0.4674) X_1172 = 1st SARAGOSSA POINT OF X(48) (0.6100, 0.3717) X_1714 = MIMOSA TRANSFORM OF X(28) (0.8848, 0.5404) X_1715 = MIMOSA TRANSFORM OF X(29) (0.7264, 0.5179) X_1779 = MIMOSA TRANSFORM OF X(1172) (0.7904, 0.5270) A B C X4 X46 X35 X47 X43 X165 X378 X580 X579 X1172 X1714 X1715 X1779 (a, b, c) = (5, 6, 7) | AB = 1

X1779 (MIMOSA TRANSFORM OF X1172) 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 \(f(a,b,c) = - (\cos A)/x + (\cos B)/y + (\cos C)/z\),\(x : y : z\) = X1172
Barycentrics: \(af(a,b,c) : bf(b,c,a) : cf(c,a,b)\)
Search Value (6, 9, 13): \(0.765108380189\)
▸ Incident Central Lines7 lines

{3, 1780}, {4, 46}, {35, 47}, {43, 165}, {378, 580}, {579, 1172}, {1714, 1715}

▸ Functional Relations1 relation