Chapter 13.1, Problem 15MC

To determine

To write:

The response to Noah when he claims he can construct the two touching circles (they have exactly one point in common) shown in figure in two different ways; by choosing a point $P$ on the circle with centre $O$ and finding its image under a half-turn about $P$ or by translating the circle with centre $O$ by $2\overrightarrow{OP}$. Consequently, he says that the image of any figure under half-turn can also be achieved by a translation.