Before even attempting to understand this app, take a look at the heptagon and nonagon versions.

It’s the same situation here, circles centered at intersection points of diagonals within the hendecagon. Drag the green points to resize the circles. Resize the circles so that they are tangent to at least 4 diagonals at the same time (this case is possible in at least two positions for each circle). How many instances can you find on this one? Notice a trend with this and the other versions?

Now that you’ve got this one, check out the final installment, the tridecagon version.