X923

POINT ALBIREO

X923 = barycentric product X1*X111
< 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) { 42, 101 }: Central Line L(42, 101) { 31, 163 }: Central Line L(31, 163) { 1, 662 }: Central Line L(1, 662) { 213, 692 }: Central Line L(213, 692) { 691, 741 }: Central Line L(691, 741) A = Vertex A (0.0000, 0.0000) B = Vertex B (1.0000, 0.0000) C = Vertex C (0.6122, 0.5999) X_42 = CROSSPOINT OF INCENTER AND SYMMEDIAN POINT (0.5880, 0.2495) X_101 = Ψ(INCENTER, SYMMEDIAN POINT) (0.2143, 0.5249) X_31 = 2nd POWER POINT (0.6228, 0.3008) X_163 = TRILINEAR PRODUCT X(6)*X(110) (0.3174, 0.5883) X_1 = INCENTER (0.5714, 0.2333) X_662 = TRILINEAR POLE OF LINE X(1)X(21) (0.1811, 0.4951) X_213 = -CEVA CONJUGATE OF X(42) (0.6135, 0.2833) X_692 = -CEVA CONJUGATE OF X(101) (0.2833, 0.5715) X_691 = TRILINEAR POLE OF LINE X(6)X(110) (1.0101, 0.0886) X_741 = EVEN (- 1, 1) CIRCUMCIRCLE POINT (1.0071, 0.0451) X_923 = POINT ALBIREO (1.0002, -0.0544) A B C X42 X101 X31 X163 X1 X662 X213 X692 X691 X741 X923 (a, b, c) = (5, 6, 7) | AB = 1

X923 (POINT ALBIREO) 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 \(f(a,b,c) = a^{2}/(b^{2} + c^{2} - 2a^{2})\) (M. Iliev, 5/13/07)
Barycentrics: \(af(a,b,c) : bf(b,c,a) : cf(c,a,b)\)
Search Value (6, 9, 13): \(1.163666744440\)
▸ Incident Central Lines5 lines

{1, 662}, {31, 163}, {42, 101}, {213, 692}, {691, 741}

▸ Functional Relations6 relations