AIME II 2009 #15

[stupidityismygam]

Let [unparseable or potentially dangerous latex formula] be a diameter of a circle with diameter [unparseable or potentially dangerous latex formula] Let [unparseable or potentially dangerous latex formula] and [unparseable or potentially dangerous latex formula] be points on one of the semicircular arcs determined by [unparseable or potentially dangerous latex formula] such that [unparseable or potentially dangerous latex formula] is the midpoint of the semicircle and [unparseable or potentially dangerous latex formula] Point [unparseable or potentially dangerous latex formula] lies on the other semicircular arc. Let [unparseable or potentially dangerous latex formula] be the length of the line segment whose endpoints are the intersections of diameter [unparseable or potentially dangerous latex formula] with the chords [unparseable or potentially dangerous latex formula] and [unparseable or potentially dangerous latex formula] The largest possible value of [unparseable or potentially dangerous latex formula] can be written in the form [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]

[sinkokuyou]

here's the picture: