## Problem of the Day #355: The Fourth SideMarch 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 $\overline{CD}$.