Question 85
Let $\mathcal{K}$ be a circle with centre $O$, and let $\mathcal{K}'$ be a circle that goes through the point $O$ with a radius that is 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 point $A$, and it touches the circle $\mathcal{K}'$ at point $B$. Let $C$ denote the mirror image of the point $B$ with respect to point $A$. The line $AO$ intersects the circle $\mathcal{K}'$ at points $O$ and $D$, and line $CD$ intersects circle $\mathcal{K}'$ at points $D$ and $E$. Prove that line $BE$ is a tangent of the circle $\mathcal{K}$.