20. Two circles with radii $R$ and $r(R>r)$ are externally tangent at point $A$. A straight line through point $B$, taken on the larger circle, is tangent to the smaller circle at point $C$. Find $|B C|$, if $|A B|=a$.
20. Draw the line $B A$ and denote by $D$ the second point of intersection with the smaller circle. Consider the arcs $A \bar{B}$ and $A \bar{D}$ (smaller than a semicircle). Since the common tangent to the circles at point $A$ forms equal angles with $A B$ and $A D$, the central angles corresponding to these arcs are equal. Therefore, $\frac{|A D|}{|A B|}=\frac{r}{R},|A D|=a \frac{r}{R},|B C|=\sqrt{|B D| \cdot|B A|}=$ $=a \sqrt{\frac{R+r}{R}}$.