X727

EVEN (- 2, -1) CIRCUMCIRCLE POINT

X727 = X238-cross conjugate of X58
< 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) { 31, 43 }: Central Line L(31, 43) { 32, 101 }: Central Line L(32, 101) { 58, 99 }: Central Line L(58, 99) { 1, 932 }: Central Line L(1, 932) { 789, 985 }: Central Line L(789, 985) { 934, 1106 }: Central Line L(934, 1106) A = Vertex A (0.0000, 0.0000) B = Vertex B (1.0000, 0.0000) C = Vertex C (0.6122, 0.5999) X_726 = EVEN (- 2, -1) INFINITY POINT (1.0187, 0.5358) X_31 = 2nd POWER POINT (0.6228, 0.3008) X_43 = -CEVA CONJUGATE OF X(1) (0.6358, 0.2963) X_32 = 3rd POWER POINT (0.6400, 0.3332) X_101 = Ψ(INCENTER, SYMMEDIAN POINT) (0.2143, 0.5249) X_58 = ISOGONAL CONJUGATE OF X(10) (0.6107, 0.2850) X_99 = STEINER POINT (0.1109, 0.4322) X_1 = INCENTER (0.5714, 0.2333) X_932 = -CROSS CONJUGATE OF X(100) (0.0354, 0.3132) X_789 = o-(- 3, 0) CIRCUMCIRCLE POINT (0.0826, 0.3957) X_985 = ISOGONAL CONJUGATE OF X(984) (0.5961, 0.2693) X_934 = -CROSS CONJUGATE OF X(57) (0.4269, 0.6071) X_1106 = TRILINEAR SQUARE OF X(56) (0.6507, 0.4375) X_727 = EVEN (- 2, -1) CIRCUMCIRCLE POINT (1.0060, 0.1685) A B C X726 X31 X43 X32 X101 X58 X99 X1 X932 X789 X985 X934 X1106 X727 (a, b, c) = (5, 6, 7) | AB = 1

X727 (EVEN (- 2, -1) CIRCUMCIRCLE POINT) 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 \(f(a,b,c) = 1/[a ^{-3}(b ^{-1} + c ^{-1}) - a ^{-2}(b ^{-2} + c ^{-2})]\)
Barycentrics: \(g(a,b,c) : g(b,c,a) : g(c,a,b)\), where \(g(a,b,c) = af(a,b,c)\)
Search Value (6, 9, 13): \(-0.618761834841\)

X727 lies on the circumcircle.

▸ Incident Central Lines6 lines

{1, 932}, {31, 43}, {32, 101}, {58, 99}, {789, 985}, {934, 1106}

▸ Functional Relations4 relations