X205

X9-CEVA CONJUGATE OF X31

X205 = X9-Ceva conjugate of X31
< 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) { 25, 41 }: Central Line L(25, 41) { 37, 48 }: Central Line L(37, 48) { 78, 101 }: Central Line L(78, 101) { 154, 220 }: Central Line L(154, 220) { 184, 213 }: Central Line L(184, 213) A = Vertex A (0.0000, 0.0000) B = Vertex B (1.0000, 0.0000) C = Vertex C (0.6122, 0.5999) X_9 = MITTENPUNKT (0.5110, 0.1615) X_31 = 2nd POWER POINT (0.6228, 0.3008) X_25 = HOMOTHETIC CENTER OF ORTHIC AND TANGENTIAL TRIANGLES (0.6329, 0.4497) X_41 = -CEVA CONJUGATE OF X(31) (0.5823, 0.2244) X_37 = CROSSPOINT OF INCENTER AND CENTROID (0.5567, 0.2158) X_48 = CROSSPOINT OF X(1) AND X(63) (0.5412, 0.1246) X_78 = ISOGONAL CONJUGATE OF X(34) (0.3835, 0.0491) X_101 = Ψ(INCENTER, SYMMEDIAN POINT) (0.2143, 0.5249) X_154 = -CEVA CONJUGATE OF X(6) (0.4807, -0.3954) X_220 = -CEVA CONJUGATE OF X(55) (0.4826, 0.1278) X_184 = INVERSE OF X(125) IN THE BROCARD CIRCLE (0.5788, 0.1496) X_213 = -CEVA CONJUGATE OF X(42) (0.6135, 0.2833) X_205 = -CEVA CONJUGATE OF X(31) (0.4813, -0.2261) A B C X9 X31 X25 X41 X37 X48 X78 X101 X154 X220 X184 X213 X205 (a, b, c) = (5, 6, 7) | AB = 1

X205 (X9-CEVA CONJUGATE OF X31) 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 \(f(a,b,c) = a^{2}[b^{2}\tan B/2 + c^{2}\tan C/2 - a^{2}\tan A/2]\)
Barycentrics: \(af(a,b,c) : bf(b,c,a) : cf(c,a,b)\)
Search Value (6, 9, 13): \(-1.788846215667\)
▸ Incident Central Lines5 lines

{25, 41}, {37, 48}, {78, 101}, {154, 220}, {184, 213}

▸ Functional Relations1 relation