Question 94
The plane $\alpha$ is tangent in the points $A_{1}$, $A_{2}$ and $A_{3}$ to three spheres with different radii $R_{1}$, $R_{2}$ and $R_{3}$ respectively, situated in the same halfspace two by two exteriorly. The plane $\beta$ is parallel to the plane $\alpha$ and intersects all three spheres so that the circles $D_{1}$, $D_{2}$ and $D_{3}$ are obtained. Find the distance between the planes $\alpha$ and $\beta$ so that the sum of the volumes $V_{1}$, $V_{2}$ and $V_{3}$ of the cones with the bases $D_{1}$, $D_{2}$, $D_{3}$ and the vertices $A_{1}$, $A_{2}$, $A_{3}$ respectively, will be the greatest.