Question 135
Let $AB\Gamma\Delta E$ be a convex pentagon with $A\hat{B}\Gamma = A\hat{E}\Delta = 90^\circ$. Suppose that the midpoint, let $M$, of the side $\Gamma\Delta$ is the circumcenter of the triangle $ABE$. Let $O$ be the circumcenter of the triangle $A\Gamma\Delta$. Prove that line $AO$ passes through the midpoint $N$ of segment $BE$.