Three tangent circles with spreadsheet
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 experiment with changing the sizes of the red and yellow circles by moving the WHITE dot, but it remains for you to prove your method of finding the size of the uncovered green area will work for any set of three mutually tangent circles like this.
The spreadsheet shows the areas of the green, red and yellow circles: GG, RR, YY. It also shows R and T.
You can use the spreadsheet to test your conjectures. (Note: the constant pi can be entered as 'pi' in the spreadsheet.)
This worksheet is a small modification of a worksheet of the same name created by Judah Schwartz: https://tube.geogebra.org/user/profile/id/25758