When two bubbles cling together in midair, their
common surface is part of a sphere whose center D lies on the
line passing through the centers of the bubbles (see the figure).
Also, ACB and ACD each have measure 60°
(a) Show that the radius r of the common face is given by
r = ab / a-b
[Hint: Use the Law of Sines together with the fact that an
angle u and its supplement 180 - u have the same sine.]
(b) Find the radius of the common face if the radii of the
bubbles are 4 cm and 3 cm.
(c) What shape does the common face take if the two
bubbles have equal radii?