from Polya - Mathematical Discovery
Three circles, each of which is tangent to the other two have their centers on a line.
If the radius of the surrounding circle is R and the length of the vertical (black) segment is T
what is the size of the green area?
You can explore this problem by moving the WHITE dot, but it remains for you to prove
your method will work for any set of three mutually tangent circles like this.

Do you regard this applet as the basis for a student task in
algebra? geometry? both? neither?
Would you give this task to middle school students?
Why or why not?