X2110

POINT KEPLER III

X2110 = isogonal conjugate of anticomplement of X36906
< 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) { 2, 11 }: Central Line L(2, 11) { 6, 292 }: Central Line L(6, 292) { 31, 1979 }: Central Line L(31, 1979) { 1185, 1977 }: Central Line L(1185, 1977) { 1423, 1740 }: Central Line L(1423, 1740) { 238, 2111 }: Central Line L(238, 2111) A = Vertex A (0.0000, 0.0000) B = Vertex B (1.0000, 0.0000) C = Vertex C (0.6122, 0.5999) X_2 = CENTROID (0.5374, 0.2000) X_11 = FEUERBACH POINT (0.7347, 0.0667) X_6 = SYMMEDIAN POINT (LEMOINE POINT, GREBE POINT) (0.6000, 0.2672) X_292 = -HIRST INVERSE OF X(291) (1.0127, 0.0417) X_31 = 2nd POWER POINT (0.6228, 0.3008) X_1979 = CROSSSUM OF PU(41) (1.3801, -0.0730) X_1185 = 2nd SARAGOSSA POINT OF X(31) (0.6116, 0.2797) X_1977 = BICENTRIC DIFFERENCE OF PU(42) (0.8105, 0.1754) X_1423 = -BETH CONJUGATE OF X(192) (0.6537, 0.3692) X_1740 = MIMOSA TRANSFORM OF X(184) (0.7017, 0.3500) X_238 = -LINE CONJUGATE OF X(37) (1.6190, 1.4775) X_2111 = -ISOCONJUGATE OF X(2110) (-0.1997, 0.7497) X_2110 = POINT KEPLER III (-0.2477, 0.7305) A B C X2 X11 X6 X292 X31 X1979 X1185 X1977 X1423 X1740 X238 X2111 X2110 (a, b, c) = (5, 6, 7) | AB = 1

X2110 (POINT KEPLER III) 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 \(f(a,b,c) = a[(b^{2} + bc + c^{2})a^{3} - (b + c)(b^{2} + c^{2})a^{2} - bc(b^{2} - bc + c^{2})a + b^{2}c^{2}(b + c)]\)
Barycentrics: \(af(a,b,c) : bf(b,c,a) : cf(c,a,b)\)
Search Value (6, 9, 13): \(2.583869282863\)
▸ Incident Central Lines9 lines

{2, 11}, {6, 292}, {31, 1979}, {238, 2111}, {365, 2119}, {672, 2117}, {1185, 1977}, {1423, 1740}, {1931, 2113}

▸ Functional Relations2 relations