X1201

3rd SARAGOSSA POINT OF X56

X1201 = crosspoint of X1 and X56
< 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) { 1, 2 }: Nagel Line { 31, 56 }: Central Line L(31, 56) { 58, 106 }: Central Line L(58, 106) { 65, 244 }: Central Line L(65, 244) { 36, 595 }: Central Line L(36, 595) { 205, 604 }: Central Line L(205, 604) A = Vertex A (0.0000, 0.0000) B = Vertex B (1.0000, 0.0000) C = Vertex C (0.6122, 0.5999) X_1 = INCENTER (0.5714, 0.2333) X_56 = EXSIMILICENTER(CIRCUMCIRCLE, INCIRCLE) (0.6316, 0.3438) X_2 = CENTROID (0.5374, 0.2000) X_31 = 2nd POWER POINT (0.6228, 0.3008) X_58 = ISOGONAL CONJUGATE OF X(10) (0.6107, 0.2850) X_106 = Λ(INCENTER, CENTROID) (1.0000, 0.0000) X_65 = ORTHOCENTER OF THE INTOUCH TRIANGLE (0.6041, 0.2933) X_244 = -LINE CONJUGATE OF X(100) (0.7857, 0.1166) X_36 = INVERSE-IN-CIRCUMCIRCLE OF INCENTER (1.3333, 1.6330) X_595 = 2nd HATZIPOLAKIS-YIU POINT (0.6456, 0.3307) X_205 = -CEVA CONJUGATE OF X(31) (0.4813, -0.2261) X_604 = -CEVA CONJUGATE OF X(31) (0.6442, 0.3744) X_1201 = 3rd SARAGOSSA POINT OF X(56) (0.6184, 0.2793) A B C X1 X56 X2 X31 X58 X106 X65 X244 X36 X595 X205 X604 X1201 (a, b, c) = (5, 6, 7) | AB = 1

X1201 (3rd SARAGOSSA POINT OF X56) 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 \(f(a,b,c) = a(b^{2} + c^{2} - 2bc + ab + ac)\) (M. Iliev, 5/13/07)
Search Value (6, 9, 13): \(0.729345945772\)
▸ Alternate Coordinates1 form

  • Trilinears: \(\csc^{2}(B/2) + \csc^{2}(C/2) : \csc^{2}(C/2) + \csc^{2}(A/2) : \csc^{2}(A/2) + \csc^{2}(B/2)\) (Randy Hutson, 9/23/2011)

▸ Incident Central Lines17 lines

{1, 2}, {3, 902}, {31, 56}, {32, 1055}, {36, 595}, {38, 960}, {58, 106}, {65, 244}, {73, 1104}, {105, 904}, {205, 604}, {213, 1015}, {409, 1178}, {500, 1064}, {748, 958}, {651, 1476}, {1279, 2293}

▸ Functional Relations5 relations

Notes

X1201 is the {X56,X1191}-harmonic conjugate of X31.