X1737

MIMOSA TRANSFORM OF X104

X1737 = midpoint of X36 and X80
< 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) { 36, 80 }: Central Line L(36, 80) { 1, 2 }: Nagel Line { 4, 46 }: Central Line L(4, 46) { 5, 65 }: Central Line L(5, 65) { 91, 225 }: Central Line L(91, 225) A = Vertex A (0.0000, 0.0000) B = Vertex B (1.0000, 0.0000) C = Vertex C (0.6122, 0.5999) X_36 = INVERSE-IN-CIRCUMCIRCLE OF INCENTER (1.3333, 1.6330) X_80 = REFLECTION OF INCENTER IN FEUERBACH POINT (0.8980, -0.1000) X_1 = INCENTER (0.5714, 0.2333) X_2 = CENTROID (0.5374, 0.2000) X_4 = ORTHOCENTER (0.6122, 0.3958) X_46 = -CEVA CONJUGATE OF X(1) (0.6917, 0.4543) X_5 = NINE-POINT CENTER (0.5561, 0.2489) X_65 = ORTHOCENTER OF THE INTOUCH TRIANGLE (0.6041, 0.2933) X_91 = ISOGONAL CONJUGATE OF X(47) (-0.0865, -0.0205) X_225 = -CEVA CONJUGATE OF X(65) (0.6246, 0.4451) X_1737 = MIMOSA TRANSFORM OF X(104) (1.1156, 0.7665) A B C X36 X80 X1 X2 X4 X46 X5 X65 X91 X225 X1737 (a, b, c) = (5, 6, 7) | AB = 1

X1737 (MIMOSA TRANSFORM OF X104) constructed on acute reference triangle \((a, b, c) = (5, 6, 7)\) with unit baseline AB = \(1\).

Constructed Elements

Trilinears: \(- (\cos A)/x + (\cos B)/y + (\cos C)/z : :\), where \(x : y : z\) = X104
Barycentrics: \(a^{3} (b + c) - a^{2} (b^{2} + c^{2}) - a (b - c)^{2} (b + c) + (b^{2} - c^{2})^{2} : :\)
Search Value (6, 9, 13): \(0.510337473187\)
▸ Alternate Coordinates1 form

  • Barycentrics: \(\sin B (\cos A + \cos B - 1) + \sin C (\cos A + \cos C - 1) : :\)

▸ Incident Central Lines32 lines

{1, 2}, {3, 1837}, {4, 46}, {5, 65}, {11, 517}, {12, 942}, {29, 1780}, {30, 1155}, {35, 950}, {36, 80}, {40, 1479}, {47, 1724}, {56, 355}, {57, 1478}, {72, 1329}, {91, 225}, {109, 1877}, {117, 1845}, {119, 912}, {150, 1447}, {240, 522}, {281, 1723}, {354, 495}, {381, 1836}, {427, 1905}, {484, 516}, {579, 1826}, {758, 908}, {952, 1319}, {1718, 1870}, {1747, 1890}, {1782, 1842}

▸ Functional Relations8 relations