Let A B C be a triangle with A B=209, A C=243, and \angle B A C=60^{\circ}, and denote by N the midpoint of the major arc \widehat{B A C} of circle \odot(A B C). Suppose the parallel to A B through N intersects \overline{B C} at a point X. Compute the ratio \frac{B X}{X C}.