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In the accompanying figure, semicircles with centers

A

and

B

have radii

4

and

2

, respectively. Furthermore, they are internally tangent to the circle of diameter

PQ

. Also the semicircles with centers

A

and

B

are externally tangent to each other. The circle with center

C

is internally tangent to the semicircle with diameter

PQ

and externally tangent to the others two semicircles. Determine the value of the radius of the circle with center

C

. https://cdn.artofproblemsolving.com/attachments/c/b/281b335f6a2d6230a5b79060e6d85d6ca6f06c.png

Problem Statement