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Tangent Circles

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Two congruent semicircles lie on the diameter of a third semicircle, each tangent to the other two. A small circle is tangent to all three semicircles. If the area of the shaded region is 45pi, what is the length of the radius of the small circle.

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Solution Summary

The radius of a circle tangent to two other circles is found.

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Please see the attached file for the complete solution.
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Let the circles be A B C D

Radius of A is 2r
B and C is r
And ...

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