Poncelet Transverse

Let a Circle $C_1$ lie inside another Circle $C_2$. From any point on $C_2$, draw a tangent to $C_1$ and extend it to $C_2$. From the point, draw another tangent, etc. For $n$ tangents, the result is called an $n$-sided Poncelet Transform.

References

Dörrie, H. 100 Great Problems of Elementary Mathematics: Their History and Solutions. New York: Dover, p. 192, 1965.