## Problem of the Day #355: The Fourth Side
*March 8, 2012*

*Posted by Saketh in : potd , trackback*

Quadrilateral $ABCD$ has $AB = BC = 5$ and $AD = 4$. If $m\angle ABD = 2 m\angle CDB$ and $m\angle CBD = 2 m\angle ADB$, find all possible values for the length of side $\overline{CD}$.

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