Question 15
Let $\triangle ABC$ be an acute-angled triangle such that $|AB| \lt |AC|$. Point $D$ is the midpoint of the shorter arc $\widehat{BC}$ of the circumcircle of the triangle $ABC$. Point $I$ is the incentre of the triangle $ABC$, and point $J$ is the reflection of $I$ across the line $BC$. Line $DJ$ intersects the circumcircle of the triangle $ABC$ at the point $E$ which lies on the shorter arc $\widehat{AB}$.
Prove that $|AI| = |IE|$ holds. (Romania 2017)
Prove that $|AI| = |IE|$ holds. (Romania 2017)