536. Given a conical funnel, the angle of the axial section of which is equal to $2 \alpha$, and two spheres of radii $\boldsymbol{R}$ and $r$. Find the necessary and sufficient conditions for both spheres to be placed in the funnel so that both are in contact with its lateral surface.
536. By making an axial section, we reduce the problem to planimetry; the required condition is:

$$
\sin \alpha \leqslant \frac{R-r}{R}
$$