X869

INTERSECTION OF LINES X1X_2 AND X31X_32

X869 = crossdifference of every pair of points on line X649X693
< 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 { 31, 32 }: Central Line L(31, 32) { 6, 292 }: Central Line L(6, 292) { 100, 731 }: Central Line L(100, 731) { 101, 743 }: Central Line L(101, 743) { 55, 893 }: Central Line L(55, 893) A = Vertex A (0.0000, 0.0000) B = Vertex B (1.0000, 0.0000) C = Vertex C (0.6122, 0.5999) X_870 = ISOGONAL CONJUGATE OF X(869) (0.5328, 0.2015) X_1 = INCENTER (0.5714, 0.2333) X_2 = CENTROID (0.5374, 0.2000) X_31 = 2nd POWER POINT (0.6228, 0.3008) X_32 = 3rd POWER POINT (0.6400, 0.3332) X_6 = SYMMEDIAN POINT (LEMOINE POINT, GREBE POINT) (0.6000, 0.2672) X_292 = -HIRST INVERSE OF X(291) (1.0127, 0.0417) X_100 = ANTICOMPLEMENT OF FEUERBACH POINT (0.1429, 0.4666) X_731 = EVEN (- 2, 1) CIRCUMCIRCLE POINT (1.0101, 0.0876) X_101 = Ψ(INCENTER, SYMMEDIAN POINT) (0.2143, 0.5249) X_743 = EVEN (- 1, 2) CIRCUMCIRCLE POINT (1.0002, 0.0008) X_55 = INSIMILICENTER(CIRCUMCIRCLE, INCIRCLE) (0.5490, 0.1921) X_893 = -CROSS CONJUGATE OF X(292) (0.5910, 0.2480) X_869 = INTERSECTION OF LINES X(1)X(2) AND X(31)X(32) (0.6039, 0.2651) A B C X870 X1 X2 X31 X32 X6 X292 X100 X731 X101 X743 X55 X893 X869 (a, b, c) = (5, 6, 7) | AB = 1

X869 (INTERSECTION OF LINES X1X_2 AND X31X_32) 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 \(f(a,b,c) = a^{2}(b^{2} + c^{2} + bc)\)
Barycentrics: \(g(a,b,c) : g(b,c,a) : g(c,a,b)\), where \(g(a,b,c) = af(a,b,c)\)
Search Value (6, 9, 13): \(0.945619416021\)
▸ Incident Central Lines9 lines

{1, 2}, {6, 292}, {31, 32}, {38, 980}, {55, 893}, {100, 731}, {101, 743}, {192, 1045}, {210, 1107}

▸ Functional Relations3 relations