Question 141
On the bases $AB$ and $CD$ of a trapezoid $ABCD$ draw two squares externally to $ABCD$. Let $O$ be the intersection point of the diagonals $AC$ and $BD$, and let $O_{1}$ and $O_{2}$ be the centers of the two squares. Prove that $O_{1}$, $O$ and $O_{2}$ lie on a line (i.e. they are collinear; see Figure.)