AIME I #10 2008

[stupidityismygam]

Let [unparseable or potentially dangerous latex formula] be an isosceles trapezoid with [unparseable or potentially dangerous latex formula] whose angle at the longer base [unparseable or potentially dangerous latex formula] is [unparseable or potentially dangerous latex formula]. The diagonals have length [unparseable or potentially dangerous latex formula] and the point [unparseable or potentially dangerous latex formula] is at distances [unparseable or potentially dangerous latex formula] and [unparseable or potentially dangerous latex formula] from vertices [unparseable or potentially dangerous latex formula] and [unparseable or potentially dangerous latex formula] respectively. Let [unparseable or potentially dangerous latex formula] be the foot of the altitude from [unparseable or potentially dangerous latex formula] to [unparseable or potentially dangerous latex formula] The distance [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 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]