Question 25
Triangle $ABC$ has $\angle BAC = 60^\circ,$ $\angle CBA \le 90^\circ,$ $BC = 1,$ and $AC \ge AB.$ Let $H,$ $I,$ and $O$ be the orthocenter, incenter, and circumcenter of $\triangle ABC,$ respectively. Assume that the area of the pentagon $BCOIH$ is the maximum possible. What is $\angle CBA?$