Question 125
Two circles $\mathcal{C}$ and $\mathcal{C}^{\prime}$ with centres $O$ and $O^{\prime}$ are externally tangent at $B$. A common external tangent touches $\mathcal{C}$ at $M$ and $\mathcal{C}^{\prime}$ at $N$. The common tangent to $\mathcal{C}$ and $\mathcal{C}^{\prime}$ at $B$ meets $(M N)$ at $A$. Let $C$ be the intersection of $(O A)$ and $(B M)$, and $D$ the intersection of $\left(O^{\prime} A\right)$ and $(B N)$.
Show that $(C D)$ is parallel to $(M N)$.
Show that $(C D)$ is parallel to $(M N)$.