Eh, I don't want to solve it now (it's very late in my time zone), so I'll just give the technique, and post the answer later. Divide square into two rectangles, use area of square, diagonals of rectangles (which are the radii of the semicircle) to find relationships between numbers, apply to full circle using the fact that full circle square's diagonal is diameter, done. Easy.
I wanna start an Olympiad or AIME topic!
