2007 AIME I Problem 12

In isosceles triangle ABC, A is located at the origin and B is located at (20,0). Point C is in the first quadrant with AC = BC and angle BAC = 75^{\circ}. If triangle ABC is rotated counterclockwise about point A until the image of C lies on the positive y-axis, the area of the region common to the original and the rotated triangle is in the form p\sqrt{2} + q\sqrt{3} + r\sqrt{6} + s, where p,q,r,s are integers. Find (p-q+r-s)/2.

Leading zeroes must be inputted, so if your answer is 34, then input 034

Full credit goes to MAA for authoring these problems. These problems were taken on the AOPS website.