MathNet 2013 Question 31

Let $ABC$ be an obtuse triangle with circumcenter $O$ such that $\angle ABC = 15^{\circ}$ and $\angle BAC \gt 90^{\circ}$. Suppose that $AO$ meets $BC$ at $D$, and that $OD^{2} + OC \cdot DC = OC^{2}$. Find $\angle C$.

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