# 2013 Mock AIME I Problems/Problem 1

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## Problem 1

Two circles and , each of unit radius, have centers and such that . Let be the midpoint of and let be a circle externally tangent to both and . and have a common tangent that passes through . If this tangent is also a common tangent to and , find the radius of circle .

## Solution

Let be the center of circle and be the point of tangency between and . Note that triangles and are similar, so and . Thus the radius of is .