X1326

INVERSE-IN-CIRCUMCIRCLE OF X58

X1326 = circumcircle-inverse 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) circumcircle: Circumcircle of △ABC { 3, 58 }: Brocard Axis { 3, 6 }: Brocard Axis { 10, 261 }: Central Line L(10, 261) { 42, 593 }: Central Line L(42, 593) { 106, 691 }: Central Line L(106, 691) A = Vertex A (0.0000, 0.0000) B = Vertex B (1.0000, 0.0000) C = Vertex C (0.6122, 0.5999) X_3 = CIRCUMCENTER (0.5000, 0.1021) X_58 = ISOGONAL CONJUGATE OF X(10) (0.6107, 0.2850) X_6 = SYMMEDIAN POINT (LEMOINE POINT, GREBE POINT) (0.6000, 0.2672) X_10 = SPIEKER CENTER (0.5204, 0.1833) X_261 = ISOTOMIC CONJUGATE OF X(12) (0.5072, 0.1625) X_42 = CROSSPOINT OF INCENTER AND SYMMEDIAN POINT (0.5880, 0.2495) X_593 = 1st HATZIPOLAKIS-YIU POINT (0.6202, 0.3026) X_106 = Λ(INCENTER, CENTROID) (1.0000, 0.0000) X_691 = TRILINEAR POLE OF LINE X(6)X(110) (1.0101, 0.0886) X_1326 = INVERSE-IN-CIRCUMCIRCLE OF X(58) (1.1309, 1.1440) A B C X3 X58 X6 X10 X261 X42 X593 X106 X691 X1326 (a, b, c) = (5, 6, 7) | AB = 1

X1326 (INVERSE-IN-CIRCUMCIRCLE OF X58) 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 \(f(a,b,c) = a(b^{2} + c^{2} - a^{2} + bc - ab - ac)/(b + c)\)
Barycentrics: \(af(a,b,c) : bf(b,c,a) : cf(c,a,b)\)
Search Value (6, 9, 13): \(-1.496298457601\)
▸ Incident Central Lines10 lines

{3, 6}, {10, 261}, {35, 849}, {42, 593}, {99, 726}, {106, 691}, {110, 902}, {238, 662}, {249, 1101}, {727, 805}

▸ Functional Relations7 relations