Question 103
The circles $\mathcal{K}_1$ and $\mathcal{K}_2$ with centres $O_1$ and $O_2$ touch externally. Let $p$ be a common tangent of the circles $\mathcal{K}_1$ and $\mathcal{K}_2$ that does not pass through their point of tangency. Prove that $p$ is also a tangent of the circle with diameter $O_1 O_2$.