X3290

INTERSECTION OF LINES X2X_37 AND X230X_231

Let L denote the line through X3 perpendicular to the line X1X6. Coefficients for a trilinear equation for L are the trilinears for X3290.
< 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) { 3125, 3230 }: Central Line L(3125, 3230) { 2, 37 }: Central Line L(2, 37) { 6, 354 }: Central Line L(6, 354) { 230, 231 }: Central Line L(230, 231) { 241, 292 }: Central Line L(241, 292) A = Vertex A (0.0000, 0.0000) B = Vertex B (1.0000, 0.0000) C = Vertex C (0.6122, 0.5999) X_3125 = DANNEELS PERSPECTOR FOR X(81) (0.7794, 0.1074) X_3230 = ISOGONAL CONJUGATE OF X(3227) (1.3535, 1.1621) X_2 = CENTROID (0.5374, 0.2000) X_37 = CROSSPOINT OF INCENTER AND CENTROID (0.5567, 0.2158) X_6 = SYMMEDIAN POINT (LEMOINE POINT, GREBE POINT) (0.6000, 0.2672) X_354 = WEILL POINT (0.5823, 0.2533) X_230 = -CEVA CONJUGATE OF X(114) (0.9746, 0.6698) X_231 = -CEVA CONJUGATE OF X(128) (1.0375, 0.6458) X_241 = -LINE CONJUGATE OF X(55) (1.1217, 1.2442) X_292 = -HIRST INVERSE OF X(291) (1.0127, 0.0417) X_3290 = INTERSECTION OF LINES X(2)X(37) AND X(230)X(231) (1.0664, 0.6348) A B C X3125 X3230 X2 X37 X6 X354 X230 X231 X241 X292 X3290 (a, b, c) = (5, 6, 7) | AB = 1

X3290 (INTERSECTION OF LINES X2X_37 AND X230X_231) constructed on acute reference triangle \((a, b, c) = (5, 6, 7)\) with unit baseline AB = \(1\).

Constructed Elements

Trilinears: \(b^{3} + c^{3} - 2abc + (a^{2} - bc)(b + c) : :\)
Search Value (6, 9, 13): \(-0.502427157800\)
▸ Incident Central Lines19 lines

{1, 2271}, {2, 37}, {6, 354}, {9, 982}, {19, 1611}, {25, 1841}, {65, 2176}, {105, 910}, {111, 1290}, {120, 1738}, {172, 1104}, {213, 942}, {230, 231}, {241, 292}, {244, 672}, {518, 2238}, {1018, 1739}, {1149, 2170}, {1212, 2275}

▸ Functional Relations13 relations