Given triangle $ABC$. Point $O_1$ is the center of the $BCDE$ rectangle, constructed so that the side $DE$ of the rectangle contains the vertex $A$ of the triangle. Points $O_2$ and $O_3$ are the centers of rectangles constructed in the same way on the sides $AC$ and $AB$, respectively. Prove that lines $AO_1, BO_2$ and $CO_3$ meet at one point.