Problem of the Week

This will be the final problem of the year.  Enjoy your summer break, and check in again in the fall for new problems from the Bradley University Problem of the Week.  

The quarter-circle has radius 1.  The semicircle has radius 1/2.  What is the radius and center of the small, red circle which is tangent to the other two and to the vertical axis?  (See figure on the left.)

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ã2003 Alberto L. Delgado