AIME I 2026 (Problem 3)
A hemisphere with radius 200 sits on top of a horizontal circular disk with radius 200, and the hemisphere and disk have the same center. Let be the region of points in the disk such that a sphere of radius 42 can be placed on top of the disk at and lie completely inside the hemisphere. The area of divided by the area of the disk is , where and are relatively prime positive integers. Find .
