15. Find the area of the rhombus $ABCD$, if the radii of the circles circumscribed around triangles $ABC$ and $ABD$ are $R$ and $r$.
15. If the acute angle of a rhombus is $\alpha$, then the diagonals of the rhombus will be $2 r \sin \alpha$ and $2 R \sin \alpha$. On the other hand, the ratio of the diagonals is the tangent of half this angle, i.e., $\operatorname{tg} \frac{\alpha}{2}=\frac{r}{R}$, $\sin \alpha=\frac{2 R r}{R^{2}+r^{2}}$.

Answer: $\frac{8 R^{3} r^{3}}{\left(R^{2}+r^{2}\right)^{2}}$.