Given an acute-angled triangle ABC in which ∣AB∣<∣AC∣. Point D is the midpoint of the shorter arc BC of its circumcircle. The point I is the center of its incircle, and the point J is symmetric point of I wrt line BC. The line DJ intersects the circumcircle of the triangle ABC at the point E belonging to the arc AB. Prove that ∣AI∣=∣IE∣. geometryincentercircumcirclearc midpoint