Cubical block on a cylinder challenging problem

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Homework Statement


A cubical block of side L rests on a fixed cylindrical drum of radius R. Find the largest value of L for which the block is stable.

This is problem 6.35 from the Kleppner+Kolenkow Introduction to Mechanics book. I honestly have no clue where to even start on this problem. Anyone care to give me a hint?
 
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Say you displace the block by an angle θ. Where's the support point? Where's the center of mass in relation to the support point?