AHSME 1979 Problem 28

Circles with centers $A ,~ B$, and $C$ each have radius $r$, where $1 < r < 2$. The distance between each pair of centers is $2$. If $B'$ is the point of intersection of circle $A$ and circle $C$ which is outside circle $B$, and if $C'$ is the point of intersection of circle $A$ and circle $B$ which is outside circle $C$, then length $B'C'$ equals $\textbf{(A) }3r-2 \textbf{(B) }r^2 \textbf{(C) }r+\sqrt{3(r-1)} \\ \textbf{(D) }1+\sqrt{3(r^2-1)} \textbf{(E) }\text{none of these}$