Mock AIME 3 Pre 2005 Problems/Problem 14
Circles and are centered on opposite sides of line , and are both tangent to at . passes through , intersecting again at . Let and be the intersections of and , and and respectively. and are extended past and intersect and at and respectively. If and , then the area of triangle can be expressed as , where and are positive integers such that and are coprime and is not divisible by the square of any prime. Determine .
Invert about a circle with radius 1 and center P. Note that since all relevant circles and lines go through P, they all are transformed into lines, and are all tangent at infinity (i.e. parallel). That was the crux move; some more basic length chasing using similar triangles gets you the answer. This problem needs a solution. If you have a solution for it, please help us out by adding it.
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