X3213

X57-CEVA CONJUGATE OF X34

X3213 = X3172-cross conjugate of X204
< 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) { 19, 56 }: Central Line L(19, 56) { 6, 208 }: Central Line L(6, 208) { 154, 204 }: Central Line L(154, 204) { 196, 380 }: Central Line L(196, 380) { 34, 604 }: Central Line L(34, 604) { 57, 1172 }: Central Line L(57, 1172) 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_34 = -BETH CONJUGATE OF X(4) (0.6332, 0.4792) X_19 = CLAWSON POINT (0.6246, 0.4244) X_56 = EXSIMILICENTER(CIRCUMCIRCLE, INCIRCLE) (0.6316, 0.3438) X_6 = SYMMEDIAN POINT (LEMOINE POINT, GREBE POINT) (0.6000, 0.2672) X_208 = -CEVA CONJUGATE OF X(34) (0.6242, -0.2728) X_154 = -CEVA CONJUGATE OF X(6) (0.4807, -0.3954) X_204 = -CEVA CONJUGATE OF X(19) (0.6683, 3.3982) X_196 = -CEVA CONJUGATE OF X(4) (0.5649, -0.1989) X_380 = INTERSECTION OF LINES X(1)X(19) AND X(9)X(55) (0.5631, 0.2035) X_604 = -CEVA CONJUGATE OF X(31) (0.6442, 0.3744) X_1172 = 1st SARAGOSSA POINT OF X(48) (0.6100, 0.3717) X_3213 = -CEVA CONJUGATE OF X(34) (0.5589, 1.1858) A B C X57 X34 X19 X56 X6 X208 X154 X204 X196 X380 X604 X1172 X3213 (a, b, c) = (5, 6, 7) | AB = 1

X3213 (X57-CEVA CONJUGATE OF X34) 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 \(u : v : w\) = X34
Barycentrics: \(ag(a,b,c) : bg(b,c,a) : cg(c,a,b)\)
Search Value (6, 9, 13): \(0.052277914039\)
▸ Alternate Coordinates1 form

  • Trilinears: \(g(a,b,c) : g(b,c,a) : g(c,a,b)\), where \(g(a,b,c) = [3a^{4} - 2a^{2}(b^{2} + c^{2}) - (b^{2} - c^{2})^{2}]/[(b + c - a)(b^{2} + c^{2} - a^{2})] (E\). Danneels)

▸ Incident Central Lines10 lines

{6, 208}, {19, 56}, {33, 2285}, {34, 604}, {48, 2331}, {57, 1172}, {154, 204}, {196, 380}, {608, 1407}, {610, 1249}

▸ Functional Relations4 relations