If you alter the drawing you provided slightly, the solution becomes
evident. Draw r1 horizontally from the origin to the right. Then draw r2
from the center of the larger circle to the same point (the right-hand
intersection of the larger circle with the x-axis). You can then see a right
triangle, and you can deduce that

r1^2 + h2^2 = r2^2

In addition, you can plainly see that h1 + h2 = r2.

You can use these two equations to solve first for h1 and then for r2.

 - Slime
 [ http://www.slimeland.com/ ]

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