AIME I 2009 #12

[stupidityismygam]

In right [unparseable or potentially dangerous latex formula] with hypotenuse [unparseable or potentially dangerous latex formula] and [unparseable or potentially dangerous latex formula] is the altitude to [unparseable or potentially dangerous latex formula] Let [unparseable or potentially dangerous latex formula] be the circle having [unparseable or potentially dangerous latex formula] as a diameter. Let [unparseable or potentially dangerous latex formula] be a point outside of [unparseable or potentially dangerous latex formula] such that [unparseable or potentially dangerous latex formula] and [unparseable or potentially dangerous latex formula] are both tangent to circle [unparseable or potentially dangerous latex formula] The ratio of the perimeter to [unparseable or potentially dangerous latex formula] to the length of [unparseable or potentially dangerous latex formula] can be expressed in the form [unparseable or potentially dangerous latex formula] where [unparseable or potentially dangerous latex formula] and [unparseable or potentially dangerous latex formula] are relatively prime positive integers. Find [unparseable or potentially dangerous latex formula]

[88bobcat]