Question 30
A trapezium $ABCD$ has $AD\parallel BC$ and a point $E$ is chosen on the base $AD$ so that the line segments $BE$ and $CE$ divide the trapezium into three right-angled triangles. These three triangles are similar, but no two are congruent. In common units, all the triangles’ side lengths are integers. The length of $AD$ is 2009. What is the length of $BC$?