Let $A,B,C$ be different points on a circle such that $AB = AC$. Point $E$ lies on the segment $BC$, and $D \ne A$ is the intersection point of the circle and line $AE$. Show that the product $AE \cdot AD$ is independent of the choice of $E$.
Problem
Source: Norwegian Mathematical Olympiad 1997 - Abel Competition p2b
Tags: isosceles, circle, Product, independent, geometry