X3305

INTERSECTION OF LINES X1X_748 AND X2X_7

X3305 = {X2,X9}-harmonic conjugate of X63
< 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) { 2, 9 }: Centroid–Gergonne Line { 2, 7 }: Centroid–Gergonne Line { 78, 405 }: Central Line L(78, 405) { 19, 469 }: Central Line L(19, 469) { 306, 344 }: Central Line L(306, 344) A = Vertex A (0.0000, 0.0000) B = Vertex B (1.0000, 0.0000) C = Vertex C (0.6122, 0.5999) X_63 = ISOGONAL CONJUGATE OF X(19) (0.4566, 0.0823) X_2 = CENTROID (0.5374, 0.2000) X_9 = MITTENPUNKT (0.5110, 0.1615) X_7 = GERGONNE POINT (0.5903, 0.2769) X_78 = ISOGONAL CONJUGATE OF X(34) (0.3835, 0.0491) X_405 = EULER LINE INTERCEPT OF LINE X(1)X(6) (0.5325, 0.1870) X_19 = CLAWSON POINT (0.6246, 0.4244) X_469 = EULER LINE INTERCEPT OF LINE X(92)X(264) (0.6071, 0.3824) X_306 = ISOTOMIC CONJUGATE OF X(27) (0.3924, 0.0579) X_344 = ISOTOMIC CONJUGATE OF X(277) (0.6218, 0.2693) X_3305 = INTERSECTION OF LINES X(1)X(748) AND X(2)X(7) (0.5216, 0.1770) A B C X63 X2 X9 X7 X78 X405 X19 X469 X306 X344 X3305 (a, b, c) = (5, 6, 7) | AB = 1

X3305 (INTERSECTION OF LINES X1X_748 AND X2X_7) constructed on acute reference triangle \((a, b, c) = (5, 6, 7)\) with unit baseline AB = \(1\).

Constructed Elements

Trilinears: \((2 + \cos A) \csc A : (2 + \cos B) \csc B : (2 + \cos C) \csc C\)
Barycentrics: \(2 + \cos A : 2 + \cos B : 2 + \cos C\)
Search Value (6, 9, 13): \(3.180738204236\)
▸ Alternate Coordinates1 form

  • Trilinears: \(\csc A + \cot(A/2) : :\)

▸ Incident Central Lines15 lines

{1, 748}, {2, 7}, {10, 1479}, {19, 469}, {21, 936}, {43, 968}, {78, 405}, {81, 1743}, {169, 857}, {200, 1621}, {210, 1001}, {306, 344}, {614, 984}, {750, 1707}, {975, 1724}

▸ Functional Relations2 relations