Question 67
Let $\mathcal{K}$ be a circle with center $O$ and $\mathcal{K}'$ a circle that passes through the point $O$ and has a radius greater than twice the radius of the circle $\mathcal{K}$. A common tangent of the circles $\mathcal{K}$ and $\mathcal{K}'$ touches the circle $\mathcal{K}$ at the point $A$ and the circle $\mathcal{K}'$ at the point $B$. Denote by $C$ the reflection of the point $B$ in the point $A$. The line $AO$ intersects the circle $\mathcal{K}'$ at the points $O$ and $D$, and the line $CD$ intersects the circle $\mathcal{K}'$ at the points $D$ and $E$. Prove that the line $BE$ is tangent to the circle $\mathcal{K}$.