Let A B C be a triangle with B C=30, A C=50, and A B=60. Circle \omega_{B} is the circle passing through A and B tangent to B C at B ; \omega_{C} is defined similarly. Suppose the tangent to \odot(A B C) at A intersects \omega_{B} and \omega_{C} for the second time at X and Y respectively. Compute X Y.