X1211

ISOGONAL CONJUGATE OF X1169

X1211 is the isogonal conjugate of X1169.
< 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) { 2, 6 }: Centroid–Symmedian Line { 10, 12 }: Central Line L(10, 12) { 120, 125 }: Central Line L(120, 125) { 37, 306 }: Central Line L(37, 306) { 9, 440 }: Central Line L(9, 440) { 257, 312 }: Central Line L(257, 312) A = Vertex A (0.0000, 0.0000) B = Vertex B (1.0000, 0.0000) C = Vertex C (0.6122, 0.5999) X_1169 = 1st SARAGOSSA POINT OF X(37) (0.6140, 0.2950) X_2 = CENTROID (0.5374, 0.2000) X_6 = SYMMEDIAN POINT (LEMOINE POINT, GREBE POINT) (0.6000, 0.2672) X_10 = SPIEKER CENTER (0.5204, 0.1833) X_12 = {X(1),X(5)}-HARMONIC CONJUGATE OF X(11) (0.5641, 0.2407) X_120 = -OF-MEDIAL-TRIANGLE (0.3204, 0.3466) X_125 = CENTER OF JERABEK HYPERBOLA (0.6803, 0.0260) X_37 = CROSSPOINT OF INCENTER AND CENTROID (0.5567, 0.2158) X_306 = ISOTOMIC CONJUGATE OF X(27) (0.3924, 0.0579) X_9 = MITTENPUNKT (0.5110, 0.1615) X_440 = COMPLEMENT OF X(27) (0.4970, 0.0943) X_257 = ISOGONAL CONJUGATE OF X(172) (0.5240, 0.1822) X_312 = ISOTOMIC CONJUGATE OF X(57) (0.4256, 0.1081) X_1211 = ISOGONAL CONJUGATE OF X(1169) (0.5137, 0.1744) A B C X1169 X2 X6 X10 X12 X120 X125 X37 X306 X9 X440 X257 X312 X1211 (a, b, c) = (5, 6, 7) | AB = 1

X1211 (ISOGONAL CONJUGATE OF X1169) 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 \(f(a,b,c) = bc(b + c)(b^{2} + c^{2} + ab + ac)\) (M. Iliev, 5/13/07)
Search Value (6, 9, 13): \(3.277221969361\)
▸ Incident Central Lines11 lines

{2, 6}, {9, 440}, {10, 12}, {37, 306}, {120, 125}, {223, 936}, {257, 312}, {278, 860}, {313, 321}, {429, 960}, {1086, 1227}

▸ Functional Relations6 relations