1995 AIME Problems/Problem 12

Problem

Pyramid $\displaystyle OABCD$ has square base $\displaystyle ABCD,$ congruent edges $\displaystyle \overline{OA}, \overline{OB}, \overline{OC},$ and $\displaystyle \overline{OD},$ and $\displaystyle \angle AOB=45^\circ.$ Let $\displaystyle \theta$ be the measure of the dihedral angle formed by faces $\displaystyle OAB$ and $\displaystyle OBC.$ Given that $\displaystyle \cos \theta=m+\sqrt{n},$ where $\displaystyle m_{}$ and $\displaystyle n_{}$ are integers, find $\displaystyle m+n.$

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1995 AIME Problems/Problem 12

Problem

Solution

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