In a circle, triangle $ABC$ is inscribed with center $O$. The angle bisectors of $\angle A$, $\angle B$, and $\angle C$ intersect at the incenter $I$ of the triangle. If $\angle BAC = 70^\circ$ and $\angle ABC = 60^\circ$, find the measure of $\angle BIC$. (Express your answer in degrees.) Let's think step by step and output the final answer within \boxed{}.
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