Question 171
Let $ABC$ be an acute triangle with circumcircle $\gamma$ and incenter $I$. Let $D$ be the midpoint of minor $\operatorname{arc} \widehat{BC}$ of $\gamma$. Let $P$ be the reflection of the incenter of $ABC$ over side $BC$. Suppose line $DP$ meets $\gamma$ again at a point $Q$ on minor $\operatorname{arc} \widehat{AB}$. Show that $AI = IQ$.