BG-MO 1994 Problem 1

Two circles $k_1(O_1,R)$ and $k_2(O_2,r)$ are given in the plane such that $R \ge \sqrt2 r$ and $$O_1O_2 =\sqrt{R^2 +r^2 - r\sqrt{4R^2 +r^2}}.$$ Let $A$ be an arbitrary point on $k_1$ . The tangents from $A$ to $k_2$ touch $k_2$ at $B$ and $C$ and intersect $k_1$ again at $D$ and $E$ , respectively. Prove that $BD \cdot CE = r^2$