X213

X6-CEVA CONJUGATE OF X42

X213 = crosspoint of X6 and 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) { 1, 6 }: Incenter–Symmedian Line { 31, 32 }: Central Line L(31, 32) { 58, 101 }: Central Line L(58, 101) { 184, 205 }: Central Line L(184, 205) { 83, 239 }: Central Line L(83, 239) { 39, 672 }: Central Line L(39, 672) A = Vertex A (0.0000, 0.0000) B = Vertex B (1.0000, 0.0000) C = Vertex C (0.6122, 0.5999) X_6 = SYMMEDIAN POINT (LEMOINE POINT, GREBE POINT) (0.6000, 0.2672) X_42 = CROSSPOINT OF INCENTER AND SYMMEDIAN POINT (0.5880, 0.2495) X_1 = INCENTER (0.5714, 0.2333) X_31 = 2nd POWER POINT (0.6228, 0.3008) X_32 = 3rd POWER POINT (0.6400, 0.3332) X_58 = ISOGONAL CONJUGATE OF X(10) (0.6107, 0.2850) X_101 = Ψ(INCENTER, SYMMEDIAN POINT) (0.2143, 0.5249) X_184 = INVERSE OF X(125) IN THE BROCARD CIRCLE (0.5788, 0.1496) X_205 = -CEVA CONJUGATE OF X(31) (0.4813, -0.2261) X_83 = CEVAPOINT OF CENTROID AND SYMMEDIAN POINT (0.5651, 0.2360) X_239 = -LINE CONJUGATE OF X(42) (4.2109, 3.7992) X_39 = BROCARD MIDPOINT (0.5778, 0.2305) X_672 = CROSSDIFFERENCE OF X(1) AND X(514) (1.9245, 2.2184) X_213 = -CEVA CONJUGATE OF X(42) (0.6135, 0.2833) A B C X6 X42 X1 X31 X32 X58 X101 X184 X205 X83 X239 X39 X672 X213 (a, b, c) = (5, 6, 7) | AB = 1

X213 (X6-CEVA CONJUGATE OF X42) constructed on acute reference triangle \((a, b, c) = (5, 6, 7)\) with unit baseline AB = \(1\).

Constructed Elements

Trilinears: \((b + c)a^{2} : (c + a)b^{2} : (a + b)c^{2}\)
Barycentrics: \((b + c)a^{3} : (c + a)b^{3} : (a + b)c^{3}\)
Search Value (6, 9, 13): \(0.727031333755\)
▸ Alternate Coordinates1 form

  • Trilinears: \(a^{2}(ar - S) : b^{2}(br - S) : c^{2}(cr - S)\)

▸ Incident Central Lines13 lines

{1, 6}, {8, 981}, {31, 32}, {39, 672}, {58, 101}, {63, 980}, {83, 239}, {100, 729}, {184, 205}, {274, 894}, {607, 1096}, {667, 875}, {692, 923}

▸ Functional Relations15 relations