Here is a problem I have been developing. Maybe somebody can
tell me if it can be solved or if more information is needed.

Three solid balls of radii a, b, and c are placed in a bowl
whose inner surface is a hemisphere of radius d.
The following information is known:

1) a < b < c < d,

2) d is large enough so that each ball touches a point on
the inner surface of the bowl,

3) a is large enough so that each ball touches the other
two balls,

4) the balls are made of the same material so that their
weights are proportional to their volumes,

5) the forces that the balls exert on each other and the
bowl are directed along the lines determined by their
centers.

After the balls come to rest, what is the angle between
the plane determined by the centers of the balls and the
horizontal in terms of a, b, c, and d ?