Question 25
Let $ABC$ be a triangle satisfying $\angle B \gt \angle C$ and let $D$ be the point on the side $AC$ such that $\angle ADC = \angle C$. Let $I$ be the incenter of $ABC$ and $E$ be the intersection of the circumcircle of $CDI$ and the line $AI$ which is not $I$. Let $P$ be the intersection of the line $BD$ and the line which is parallel to $AB$ and passing $E$. Let $J$ be the incenter of $ABD$ and $A'$ be the reflection of $A$ with respect to $I$. Suppose that two lines $JP$ and $A'C$ meet at the point $Q$. Show that $QJ = QA'$.