Problem

Source: 2003 Estonia National Olympiad Final Round grade 12 p3

Tags: angle, right triangle, geometry



Let $ABC$ be a triangle with $\angle C = 90^o$ and $D$ a point on the ray $CB$ such that $|AC| \cdot |CD| = |BC|^2$. A parallel line to $AB$ through $D$ intersects the ray $CA$ at $E$. Find $\angle BEC$.