In the rectangle $ABCD$ with $|AB|<2 |AD|$, let $E$ be the midpoint of $AB$ and $F$ a point on the chord $CE$ such that $\angle CFD = 90^o$. Prove that $FAD$ is an isosceles triangle.
Problem
Source: 2003 Estonia National Olympiad Final Round grade 9 p3
Tags: geometry, rectangle, right triangle, isosceles