When 2 soap bubbles meet, you get a dividing wall between the soap bubbles. Plateau concluded that the three spheres (2 soap bubbles and the dividing wall) meet at angles of 120.
Here's an example of a construction of the dividing wall:
It is not explained exactly what is done here, figuring it out is left as an exercise to the reader. As you can see, they construction a dividing wall, which is basically part of circle which has $C$ as its center. So later on in the hand-out they ask you the following question:
Construct the dividing wall of soap bubbles with $r=3$ and $r=2$. You are given the formula $\dfrac{1}{s} = \dfrac{1}{r} + \dfrac{1}{t}$, where $r$ is the radius of the biggest bubble, $s$ is the radius of the smallest bubble and $t$ is the radius of the dividing wall.
I'm having trouble doing this, mainly because I don't fully understand the picture. This is what I do understand:
Using the formula above, we know that the radius of the dividing wall must be $6$.
We draw the biggest circle, with center $A$ and radius $3$.
We draw a line $AD$, and the tangent to $D$, so we know the angle is 90 degrees ($D_2$ in the pic). We can then draw a 120 degrees angle, like in the pic: $D_2 + D_3$.
We make another 120 degrees angle, which in the drawing would be $D_1$ + the unmarked part of $D$.
But here's where I'm stumped. How do I continue?
$DB$ is the radius of the smaller circle, thus perpendicular to one of the three $120°$ lines. Its length is given, so you can construct B.
$DC$ is the radius of the circle of which the dividing wall is part, hence perpendicular to another of the three $120°$ lines, and by symmetry $C$ is on the same line as $A$ and $B$. Thus, you should be able to construct C even without knowing the radius of the dividing wall's circle.