# Mock AIME II 2012 Problems/Problem 8

Revision as of 03:11, 5 April 2012 by Testingtesting (talk | contribs) (Created page with "==Problem== Let <math>A</math> be a point outside circle <math>\Omega</math> with center <math>O</math> and radius <math>9</math> such that the tangents from <math>A</math> to <...")

## Problem

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 .

## Solution

Let intersect at . Note that , thus . Then we have . We can use the law of cosines to find , . Thus, we have .