In honour of I.F.Sharygin.

Let $O$ and $H$ be the circumcenter and the orthocenter of a $\triangle ABC$ respectively. The line passing through the midpoint of $OH$ and parallel to $BC$ meets $AB$ and $AC$ at points $D$ and $E$ respectively. It is known that $O$ is the incenter of $\triangle ADE$ . Find the measure of $\angle A$ in degree measures.

Source:- SGO Class 8..