Question 105
Let $ABC$ be an acute-angled triangle with incentre $I$. Draw a line perpendicular to $BI$ at $I$ and let it intersect $BC$ and $BA$ at $D$ and $E$ respectively. Let $P$ and $Q$ be respectively the incentres of the triangles $BIA$ and $BIC$. Suppose the four points $D, E, P, Q$ are concyclic. Prove that $BA = BC$.