X1751

MIMOSA TRANSFORM OF X272

X1751 = cevapoint of X11 and X652
< 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) { 10, 55 }: Central Line L(10, 55) { 6, 226 }: Central Line L(6, 226) { 2, 272 }: Central Line L(2, 272) { 9, 321 }: Central Line L(9, 321) { 76, 333 }: Central Line L(76, 333) { 57, 379 }: Central Line L(57, 379) A = Vertex A (0.0000, 0.0000) B = Vertex B (1.0000, 0.0000) C = Vertex C (0.6122, 0.5999) X_11 = FEUERBACH POINT (0.7347, 0.0667) X_652 = CROSSDIFFERENCE OF X(1) AND X(4) (7.2558, -0.6836) X_10 = SPIEKER CENTER (0.5204, 0.1833) X_55 = INSIMILICENTER(CIRCUMCIRCLE, INCIRCLE) (0.5490, 0.1921) X_6 = SYMMEDIAN POINT (LEMOINE POINT, GREBE POINT) (0.6000, 0.2672) X_226 = -CEVA CONJUGATE OF X(65) (0.5778, 0.2588) X_2 = CENTROID (0.5374, 0.2000) X_272 = ISOGONAL CONJUGATE OF X(209) (-0.2458, -0.0534) X_9 = MITTENPUNKT (0.5110, 0.1615) X_321 = ISOTOMIC CONJUGATE OF X(81) (0.4800, 0.1527) X_76 = 3rd BROCARD POINT (0.4567, 0.1388) X_333 = CEVAPOINT OF X(8) AND X(9) (0.4886, 0.1475) X_57 = ISOGONAL CONJUGATE OF X(9) (0.6138, 0.3110) X_379 = EULER LINE INTERCEPT OF LINE X(6)X(7) (0.5733, 0.2937) X_1751 = MIMOSA TRANSFORM OF X(272) (-0.2166, -0.0439) A B C X11 X652 X10 X55 X6 X226 X2 X272 X9 X321 X76 X333 X57 X379 X1751 (a, b, c) = (5, 6, 7) | AB = 1

X1751 (MIMOSA TRANSFORM OF X272) 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 \(f(a,b,c) = - (\cos A)/x + (\cos B)/y + (\cos C)/z\),\(x : y : z\) = X272
Barycentrics: \(af(a,b,c) : bf(b,c,a) : cf(c,a,b)\)
Search Value (6, 9, 13): \(0.906595576220\)
▸ Incident Central Lines11 lines

{2, 272}, {4, 580}, {6, 226}, {9, 321}, {10, 55}, {19, 1708}, {27, 579}, {57, 379}, {76, 333}, {92, 1731}, {1479, 1794}

▸ Functional Relations6 relations