X3215

X57-CEVA CONJUGATE OF X48

X3215 = X57-Ceva conjugate of X48
< 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) { 3, 73 }: Central Line L(3, 73) { 34, 46 }: Central Line L(34, 46) { 31, 65 }: Central Line L(31, 65) { 6, 1195 }: Central Line L(6, 1195) { 283, 1038 }: Central Line L(283, 1038) { 224, 1331 }: Central Line L(224, 1331) A = Vertex A (0.0000, 0.0000) B = Vertex B (1.0000, 0.0000) C = Vertex C (0.6122, 0.5999) X_57 = ISOGONAL CONJUGATE OF X(9) (0.6138, 0.3110) X_48 = CROSSPOINT OF X(1) AND X(63) (0.5412, 0.1246) X_3 = CIRCUMCENTER (0.5000, 0.1021) X_73 = CROSSPOINT OF INCENTER AND CIRCUMCENTER (0.5487, 0.1428) X_34 = -BETH CONJUGATE OF X(4) (0.6332, 0.4792) X_46 = -CEVA CONJUGATE OF X(1) (0.6917, 0.4543) X_31 = 2nd POWER POINT (0.6228, 0.3008) X_65 = ORTHOCENTER OF THE INTOUCH TRIANGLE (0.6041, 0.2933) X_6 = SYMMEDIAN POINT (LEMOINE POINT, GREBE POINT) (0.6000, 0.2672) X_1195 = 3rd SARAGOSSA POINT OF X(19) (0.6245, 0.2796) X_283 = -CROSS CONJUGATE OF X(21) (0.4475, 0.0704) X_1038 = INTERSECTION OF LINES X(1)X(3) AND X(2)X(34) (0.5104, 0.1211) X_224 = -CEVA CONJUGATE OF X(63) (1.2479, 0.4419) X_1331 = ORTHOCORRESPONDENT OF X(101) (-0.2308, 0.2512) X_3215 = -CEVA CONJUGATE OF X(48) (0.8436, 0.3897) A B C X57 X48 X3 X73 X34 X46 X31 X65 X6 X1195 X283 X1038 X224 X1331 X3215 (a, b, c) = (5, 6, 7) | AB = 1

X3215 (X57-CEVA CONJUGATE OF X48) constructed on acute reference triangle \((a, b, c) = (5, 6, 7)\) with unit baseline AB = \(1\).

Constructed Elements

Trilinears: \(u(-u/x + v/y + w/z) : v(u/x - v/y + w/z) : w(u/x + v/y - w/z)\), where \(x : y : z\) = X57 and \(u : v : w\) = X48
Barycentrics: \(ag(a,b,c) : bg(b,c,a) : cg(c,a,b)\)
Search Value (6, 9, 13): \(0.508692610053\)
▸ Alternate Coordinates1 form

  • Trilinears: \(g(a,b,c) : g(b,c,a) : g(c,a,b)\), where \(g(a,b,c) = a^{2}(b^{2} + c^{2} - a^{2})[a^{3} - a^{2}(b + c) - a(b + c)^{2} + (b + c)(b^{2} + c^{2})]/(b + c - a) (E\). Danneels)

▸ Incident Central Lines17 lines

{3, 73}, {6, 1195}, {31, 65}, {34, 46}, {41, 2253}, {221, 2361}, {224, 1331}, {225, 1754}, {283, 1038}, {377, 1935}, {582, 1465}, {602, 1457}, {1496, 2646}, {1708, 1780}, {1724, 1877}, {1726, 1825}, {2199, 2245}

▸ Functional Relations1 relation