X1461

X651-BETH CONJUGATE OF X651

X1461 = barycentric product of circumcircle intercepts of the Soddy line
< 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) { 77, 572 }: Central Line L(77, 572) { 101, 651 }: Central Line L(101, 651) { 109, 692 }: Central Line L(109, 692) { 269, 604 }: Central Line L(269, 604) { 6, 911 }: Central Line L(6, 911) { 57, 909 }: Central Line L(57, 909) A = Vertex A (0.0000, 0.0000) B = Vertex B (1.0000, 0.0000) C = Vertex C (0.6122, 0.5999) X_651 = TRILINEAR POLE OF LINE X(1)X(3) (0.3048, 0.5599) X_77 = ISOGONAL CONJUGATE OF X(33) (0.5270, 0.1305) X_572 = ORTHOGONAL OF X(58) (7.2953, -0.6907) X_101 = Ψ(INCENTER, SYMMEDIAN POINT) (0.2143, 0.5249) X_109 = Ψ(INCENTER, CIRCUMCENTER) (0.3636, 0.5938) X_692 = -CEVA CONJUGATE OF X(101) (0.2833, 0.5715) X_269 = ISOGONAL CONJUGATE OF X(200) (0.6369, 0.3847) X_604 = -CEVA CONJUGATE OF X(31) (0.6442, 0.3744) X_6 = SYMMEDIAN POINT (LEMOINE POINT, GREBE POINT) (0.6000, 0.2672) X_911 = POINT ADHARA (0.8698, -0.4452) X_57 = ISOGONAL CONJUGATE OF X(9) (0.6138, 0.3110) X_909 = POINT ADHAFERA (0.9286, -0.3499) X_1461 = -BETH CONJUGATE OF X(651) (0.4656, 0.6221) A B C X651 X77 X572 X101 X109 X692 X269 X604 X6 X911 X57 X909 X1461 (a, b, c) = (5, 6, 7) | AB = 1

X1461 (X651-BETH CONJUGATE OF X651) 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 \(f(a,b,c) = (1 - \cos A)u(a,b,c)\), where \(u : v : w\) = X651
Barycentrics: \(af(a,b,c) : bf(b,c,a) : cf(c,a,b)\)
Search Value (6, 9, 13): \(0.019804376914\)
▸ Incident Central Lines15 lines

{6, 911}, {48, 1419}, {57, 909}, {58, 1410}, {77, 572}, {101, 651}, {109, 692}, {269, 604}, {284, 1439}, {514, 653}, {658, 662}, {913, 1435}, {923, 1042}, {1025, 1332}, {1412, 1427}

▸ Functional Relations7 relations