X872

INTERSECTION OF LINES X37X_42 AND X43X_75

X872 = X42-Ceva conjugate of (1500)
< 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) { 37, 42 }: Central Line L(37, 42) { 43, 75 }: Central Line L(43, 75) { 6, 292 }: Central Line L(6, 292) { 41, 560 }: Central Line L(41, 560) { 688, 798 }: Central Line L(688, 798) { 190, 1045 }: Central Line L(190, 1045) A = Vertex A (0.0000, 0.0000) B = Vertex B (1.0000, 0.0000) C = Vertex C (0.6122, 0.5999) X_873 = ISOGONAL CONJUGATE OF X(872) (0.5339, 0.2011) X_37 = CROSSPOINT OF INCENTER AND CENTROID (0.5567, 0.2158) X_42 = CROSSPOINT OF INCENTER AND SYMMEDIAN POINT (0.5880, 0.2495) X_43 = -CEVA CONJUGATE OF X(1) (0.6358, 0.2963) X_75 = ISOTOMIC CONJUGATE OF INCENTER (0.4988, 0.1682) X_6 = SYMMEDIAN POINT (LEMOINE POINT, GREBE POINT) (0.6000, 0.2672) X_292 = -HIRST INVERSE OF X(291) (1.0127, 0.0417) X_41 = -CEVA CONJUGATE OF X(31) (0.5823, 0.2244) X_560 = 4th POWER POINT (0.6520, 0.3639) X_688 = CROSSDIFFERENCE OF X(6) AND X(76) (1.0103, -0.1475) X_798 = CROSSDIFFERENCE OF X(1) AND X(75) (-13.4299, 10.5763) X_190 = YFF PARABOLIC POINT (0.0748, 0.3999) X_1045 = -CEVA CONJUGATE OF X(1) (0.6065, 0.2647) X_872 = INTERSECTION OF LINES X(37)X(42) AND X(43)X(75) (0.6029, 0.2656) A B C X873 X37 X42 X43 X75 X6 X292 X41 X560 X688 X798 X190 X1045 X872 (a, b, c) = (5, 6, 7) | AB = 1

X872 (INTERSECTION OF LINES X37X_42 AND X43X_75) constructed on acute reference triangle \((a, b, c) = (5, 6, 7)\) with unit baseline AB = \(1\).

Constructed Elements

Trilinears: \([a(b + c)]^{2} : :\)
Search Value (6, 9, 13): \(0.956633226291\)
▸ Incident Central Lines8 lines

{6, 292}, {37, 42}, {41, 560}, {43, 75}, {190, 1045}, {386, 984}, {688, 798}, {740, 1089}

▸ Functional Relations6 relations