X3217

X58-CEVA CONJUGATE OF X55

X3217 = crosssum of X514 and X3020
< 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) { 9, 21 }: Central Line L(9, 21) { 44, 48 }: Central Line L(44, 48) { 101, 604 }: Central Line L(101, 604) { 198, 672 }: Central Line L(198, 672) { 6, 1201 }: Central Line L(6, 1201) { 218, 1400 }: Central Line L(218, 1400) A = Vertex A (0.0000, 0.0000) B = Vertex B (1.0000, 0.0000) C = Vertex C (0.6122, 0.5999) X_58 = ISOGONAL CONJUGATE OF X(10) (0.6107, 0.2850) X_55 = INSIMILICENTER(CIRCUMCIRCLE, INCIRCLE) (0.5490, 0.1921) X_9 = MITTENPUNKT (0.5110, 0.1615) X_21 = SCHIFFLER POINT (0.5287, 0.1771) X_44 = -LINE CONJUGATE OF X(1) (2.1429, 2.0996) X_48 = CROSSPOINT OF X(1) AND X(63) (0.5412, 0.1246) X_101 = Ψ(INCENTER, SYMMEDIAN POINT) (0.2143, 0.5249) X_604 = -CEVA CONJUGATE OF X(31) (0.6442, 0.3744) X_198 = -CEVA CONJUGATE OF X(6) (0.4741, -0.0381) X_672 = CROSSDIFFERENCE OF X(1) AND X(514) (1.9245, 2.2184) X_6 = SYMMEDIAN POINT (LEMOINE POINT, GREBE POINT) (0.6000, 0.2672) X_1201 = 3rd SARAGOSSA POINT OF X(56) (0.6184, 0.2793) X_218 = -CEVA CONJUGATE OF X(55) (0.6557, 0.3333) X_1400 = -BETH CONJUGATE OF X(37) (0.6246, 0.3268) X_3217 = -CEVA CONJUGATE OF X(55) (0.7218, 0.3473) A B C X58 X55 X9 X21 X44 X48 X101 X604 X198 X672 X6 X1201 X218 X1400 X3217 (a, b, c) = (5, 6, 7) | AB = 1

X3217 (X58-CEVA CONJUGATE OF X55) 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 \(f(a,b,c) = a(b + c - a)(a^{2} + ab + ac - 2bc)\) (M. Iliev, 5/13/07)
Barycentrics: \(af(a,b,c) : bf(b,c,a) : cf(c,a,b)\)
Search Value (6, 9, 13): \(-2.374827768989\)
▸ Incident Central Lines16 lines

{6, 1201}, {9, 21}, {19, 1830}, {37, 2280}, {44, 48}, {101, 604}, {169, 2171}, {198, 672}, {218, 1400}, {219, 2347}, {220, 2269}, {391, 2329}, {644, 3169}, {1802, 2264}, {2174, 2267}, {2183, 2911}

▸ Functional Relations2 relations