Let $O$ be the point of intersection of the diagonals of the trapezoid $ABCD$ with the bases $AB$ and $CD$. It is known that $\angle AOB = \angle DAB = 90^o$. On the sides $AD$ and $BC$ take the points $E$ and $F$ so that $EF\parallel AB$ and $EF = AD$. Find the angle $\angle AOE$.
Problem
Source: 2005 All-Ukrainian Correspondence MO of magazine ''In the World of Mathematics'', grades 5-11 p7
Tags: geometry, trapezoid, angles, right angle, Ukraine Correspondence