X1953

BICENTRIC SUM OF PU(21)

X1953 = crosspoint of X1 and X92
< 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, 19 }: Central Line L(1, 19) { 71, 517 }: Central Line L(71, 517) { 65, 1108 }: Central Line L(65, 1108) { 9, 1389 }: Central Line L(9, 1389) { 6, 1411 }: Central Line L(6, 1411) { 216, 1393 }: Central Line L(216, 1393) 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_19 = CLAWSON POINT (0.6246, 0.4244) X_71 = ISOGONAL CONJUGATE OF X(27) (0.4807, 0.0915) X_517 = ISOGONAL CONJUGATE OF X(104) (0.8180, 0.7154) X_65 = ORTHOCENTER OF THE INTOUCH TRIANGLE (0.6041, 0.2933) X_1108 = CROSSPOINT OF X(2) AND X(84) (0.6346, 0.3084) X_9 = MITTENPUNKT (0.5110, 0.1615) X_1389 = ISOGONAL CONJUGATE OF X(1385) (0.5985, 0.3054) X_6 = SYMMEDIAN POINT (LEMOINE POINT, GREBE POINT) (0.6000, 0.2672) X_1411 = -BETH CONJUGATE OF X(80) (1.0110, -0.2153) X_216 = -CEVA CONJUGATE OF X(51) (0.5201, 0.1353) X_1393 = -BETH CONJUGATE OF X(5) (0.6196, 0.3615) X_1953 = BICENTRIC SUM OF PU(21) (0.5856, 0.2841) A B C X1 X19 X71 X517 X65 X1108 X9 X1389 X6 X1411 X216 X1393 X1953 (a, b, c) = (5, 6, 7) | AB = 1

X1953 (BICENTRIC SUM OF PU(21)) constructed on acute reference triangle \((a, b, c) = (5, 6, 7)\) with unit baseline AB = \(1\).

Constructed Elements

Trilinears: \(\sin 2B + \sin 2C : :\)
Search Value (6, 9, 13): \(0.260147610810\)
▸ Alternate Coordinates4 forms

  • Trilinears: \(\sin A \cos(B - C) : :\)

  • Trilinears: \(a^{2}(b^{2} + c^{2}) - (b^{2} - c^{2})^{2} : :\)

  • Trilinears: \(\cot B \cot C + 1 : :\)

  • Trilinears: \(S_{B}\)\(S_{C}\) + \(S^{2}\) : \(S_{C}\)\(S_{A}\) + \(S^{2}\) : :

▸ Incident Central Lines15 lines

{1, 19}, {6, 1411}, {9, 1389}, {31, 1820}, {37, 2183}, {38, 1755}, {65, 1108}, {71, 517}, {73, 1841}, {216, 1393}, {219, 1482}, {515, 1839}, {946, 1826}, {991, 1414}, {1457, 1880}

▸ Functional Relations11 relations