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Problem of the Day #353: Circles in Circles March 6, 2012

Posted by Alex in : potd , trackback

Circle $O$ with radius $16$ is internally tangent to circles $A$, $B$, and $C$. Circles $A$, $B$, and $C$ do not overlap. Circle $C$ has radius $11$ and the radii of circles $A$, $B$, and $C$ (in that order) form an increasing arithmetic sequence. Find the sum of the radii of circles $A$, $B$, and $C$.

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