AIME I 2010 #13

[stupidityismygam]

Rectangle [unparseable or potentially dangerous latex formula] and a semicircle with diameter [unparseable or potentially dangerous latex formula] are coplanar and have nonoverlapping interiors. Let [unparseable or potentially dangerous latex formula] denote the region enclosed by the semicircle and the rectangle. Line [unparseable or potentially dangerous latex formula] meets the semicircle, segment [unparseable or potentially dangerous latex formula], and segment [unparseable or potentially dangerous latex formula] at distinct points [unparseable or potentially dangerous latex formula] and [unparseable or potentially dangerous latex formula] respectively. Line [unparseable or potentially dangerous latex formula] divides region [unparseable or potentially dangerous latex formula] into two region with areas in the ratio [unparseable or potentially dangerous latex formula] Suppose that [unparseable or potentially dangerous latex formula] and [unparseable or potentially dangerous latex formula] Then [unparseable or potentially dangerous latex formula] can be represented as [unparseable or potentially dangerous latex formula], where [unparseable or potentially dangerous latex formula] and [unparseable or potentially dangerous latex formula] are positive integers and [unparseable or potentially dangerous latex formula] is not divisible by the square of any prime. Find [unparseable or potentially dangerous latex formula].

[88bobcat]

[stupidityismygam]