Mock AIME II 2012 Problems/Problem 8
Let be a point outside circle with center and radius such that the tangents from to , and , form . Let first intersect the circle at , and extend the parallel to from to meet the circle at . The length , where ,, and are positive integers and is not divisible by the square of any prime. Find .
Let intersect at . Note that , thus . Then we have . We can use the law of cosines to find , . Thus, we have .