X1462

X673-BETH CONJUGATE OF X673

X1462 = trilinear pole of line X56X667
< 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) { 6, 7 }: Central Line L(6, 7) { 31, 57 }: Central Line L(31, 57) { 269, 604 }: Central Line L(269, 604) { 213, 1170 }: Central Line L(213, 1170) { 241, 1279 }: Central Line L(241, 1279) { 739, 927 }: Central Line L(739, 927) A = Vertex A (0.0000, 0.0000) B = Vertex B (1.0000, 0.0000) C = Vertex C (0.6122, 0.5999) X_673 = TRILINEAR POLE OF LINE X(1)X(514) (0.9471, -0.0769) X_6 = SYMMEDIAN POINT (LEMOINE POINT, GREBE POINT) (0.6000, 0.2672) X_7 = GERGONNE POINT (0.5903, 0.2769) X_31 = 2nd POWER POINT (0.6228, 0.3008) X_57 = ISOGONAL CONJUGATE OF X(9) (0.6138, 0.3110) X_269 = ISOGONAL CONJUGATE OF X(200) (0.6369, 0.3847) X_604 = -CEVA CONJUGATE OF X(31) (0.6442, 0.3744) X_213 = -CEVA CONJUGATE OF X(42) (0.6135, 0.2833) X_1170 = 1st SARAGOSSA POINT OF X(41) (0.6064, 0.2908) X_241 = -LINE CONJUGATE OF X(55) (1.1217, 1.2442) X_1279 = MIDPOINT OF X(1) AND X(238) (1.0952, 0.8554) X_739 = EVEN (- 1, 0) CIRCUMCIRCLE POINT (1.0101, 0.0884) X_927 = ISOGONAL CONJUGATE OF X(926) (1.0037, 0.1836) X_1462 = -BETH CONJUGATE OF X(673) (1.0265, -0.1555) A B C X673 X6 X7 X31 X57 X269 X604 X213 X1170 X241 X1279 X739 X927 X1462 (a, b, c) = (5, 6, 7) | AB = 1

X1462 (X673-BETH CONJUGATE OF X673) 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 \(f(a,b,c) = (1 - \cos A)u(a,b,c)\), where \(u : v : w\) = X673
Barycentrics: \(af(a,b,c) : bf(b,c,a) : cf(c,a,b)\)
Search Value (6, 9, 13): \(-0.466950505205\)
▸ Incident Central Lines13 lines

{6, 7}, {31, 57}, {213, 1170}, {241, 1279}, {269, 604}, {479, 1407}, {608, 1119}, {739, 927}, {919, 1465}, {934, 1015}, {1014, 1333}, {1428, 1456}, {1429, 1458}

▸ Functional Relations6 relations