Question 151
Let $ABC$ be an acute-angled triangle. A circle $\omega_{1}(O_{1}, R_{1})$ passes through points $B$ and $C$ and meets the sides $AB$ and $AC$ at points $D$ and $E$, respectively. Let $\omega_{2}(O_{2}, R_{2})$ be the circumcircle of the triangle $ADE$. Prove that $O_{1}O_{2}$ is equal to the circumradius of the triangle $ABC$.
