X1766

MIMOSA TRANSFORM OF X345

X1766 = reflection of X990 in X3
< 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) { 990, 3 }: Central Line L(990, 3) { 4, 9 }: Orthocenter–Spieker Line { 3, 37 }: Central Line L(3, 37) { 20, 346 }: Central Line L(20, 346) { 63, 321 }: Central Line L(63, 321) A = Vertex A (0.0000, 0.0000) B = Vertex B (1.0000, 0.0000) C = Vertex C (0.6122, 0.5999) X_990 = INTERSECTION OF LINES X(1)X(7) AND X(3)X(37) (0.6104, 0.3234) X_3 = CIRCUMCENTER (0.5000, 0.1021) X_4 = ORTHOCENTER (0.6122, 0.3958) X_9 = MITTENPUNKT (0.5110, 0.1615) X_37 = CROSSPOINT OF INCENTER AND CENTROID (0.5567, 0.2158) X_20 = DE LONGCHAMPS POINT (0.3878, -0.1916) X_346 = ISOTOMIC CONJUGATE OF X(279) (0.3948, 0.0827) X_63 = ISOGONAL CONJUGATE OF X(19) (0.4566, 0.0823) X_321 = ISOTOMIC CONJUGATE OF X(81) (0.4800, 0.1527) X_1766 = MIMOSA TRANSFORM OF X(345) (0.3896, -0.1193) A B C X990 X3 X4 X9 X37 X20 X346 X63 X321 X1766 (a, b, c) = (5, 6, 7) | AB = 1

X1766 (MIMOSA TRANSFORM OF X345) 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 \(f(a,b,c) = - (\cos A)/x + (\cos B)/y + (\cos C)/z\),\(x : y : z\) = X345
Barycentrics: \(af(a,b,c) : bf(b,c,a) : cf(c,a,b)\)
Search Value (6, 9, 13): \(14.951547088197\)
▸ Incident Central Lines16 lines

{1, 572}, {3, 37}, {4, 9}, {6, 517}, {20, 346}, {46, 1400}, {63, 321}, {101, 610}, {165, 846}, {190, 1760}, {329, 1763}, {355, 594}, {672, 1723}, {971, 1350}, {1100, 1482}, {1158, 1761}

▸ Functional Relations5 relations