BALKAN 1987 Problem 4

Two circles $K_{1}$ and $K_{2}$ , centered at $O_{1}$ and $O_{2}$ with radii $1$ and $\sqrt{2}$ respectively, intersect at $A$ and $B$ . Let $C$ be a point on $K_{2}$ such that the midpoint of $AC$ lies on $K_{1}$ . Find the length of the segment $AC$ if $O_{1}O_{2}=2$