(related to Problem: The Crescent Puzzle)
Referring to the original diagram, let $AC$ be $x,$ let $CD$ be $x - 9,$ and let $EC$ be $x - 5.$ Then $x - 5$ is a mean proportional between $x - 9$ and $x,$ from which we find that $x$ equals $25.$ Therefore the diameters are $50$ in. and $41$ in. respectively.
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