In this exercise we will investigate a construction that will allow us to copy a circle with a collapsing compass. Given a circle $c$ with center $O$ and radius point $A$ and another point $B$, we wish to construct a circle centered at $B$ of radius $O A$. It suffices to prove the result for the case where $B$ is outside c. (Why?) First, construct a circle centered at $O$ of radius $O B$. Then construct a circle at $B$ of radius $O B$. Let $C$ and $D$ be the intersection points of these circles. Let $E$ be an intersection of the circle centered at $B$ with the original circle $c$.
(FIGURE CAN'T COPY)
At intersection point $C$, construct a circle of radius CE. This circle will intersect the circle at $B$ of radius $O B$ at a point $G$. Show that the circle with center $B$ and radius point $G$ is the desired circle. Why is this construction valid for a collapsing compass?