X3240

INTERSECTION OF LINES X1X_2 AND X6X_100

X3240 = crossdifference of every pair of points on the line X649X891
< 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) { 1, 2 }: Nagel Line { 6, 100 }: Central Line L(6, 100) { 89, 291 }: Central Line L(89, 291) { 44, 751 }: Central Line L(44, 751) { 192, 872 }: Central Line L(192, 872) { 88, 1002 }: Central Line L(88, 1002) A = Vertex A (0.0000, 0.0000) B = Vertex B (1.0000, 0.0000) C = Vertex C (0.6122, 0.5999) X_1 = INCENTER (0.5714, 0.2333) X_2 = CENTROID (0.5374, 0.2000) X_6 = SYMMEDIAN POINT (LEMOINE POINT, GREBE POINT) (0.6000, 0.2672) X_100 = ANTICOMPLEMENT OF FEUERBACH POINT (0.1429, 0.4666) X_89 = ISOGONAL CONJUGATE OF X(45) (0.5963, 0.2697) X_291 = 2nd SHARYGIN POINT (1.0249, 0.0364) X_44 = -LINE CONJUGATE OF X(1) (2.1429, 2.0996) X_751 = ISOGONAL CONJUGATE OF X(750) (0.5754, 0.2311) X_192 = -CEVA CONJUGATE OF X(2) (CONGRUENT PARALLELIANS POINT) (0.6147, 0.2635) X_872 = INTERSECTION OF LINES X(37)X(42) AND X(43)X(75) (0.6029, 0.2656) X_88 = ISOGONAL CONJUGATE OF X(44) (1.0000, 0.0000) X_1002 = ISOGONAL CONJUGATE OF X(1001) (0.5967, 0.2704) X_3240 = INTERSECTION OF LINES X(1)X(2) AND X(6)X(100) (0.6042, 0.2654) A B C X1 X2 X6 X100 X89 X291 X44 X751 X192 X872 X88 X1002 X3240 (a, b, c) = (5, 6, 7) | AB = 1

X3240 (INTERSECTION OF LINES X1X_2 AND X6X_100) constructed on acute reference triangle \((a, b, c) = (5, 6, 7)\) with unit baseline AB = \(1\).

Constructed Elements

Trilinears: \(bc - 2a(b + c) : :\)
Search Value (6, 9, 13): \(0.912314427606\)
▸ Incident Central Lines11 lines

{1, 2}, {6, 100}, {44, 751}, {45, 2238}, {81, 1376}, {88, 1002}, {89, 291}, {192, 872}, {218, 1005}, {238, 2177}, {1013, 1783}

▸ Functional Relations2 relations