Originally Posted by

**ellensius** I really like this graph, it was a nice find. Thanks for posting!

Actually I took for granted that Pims suggestion was correct. But it is only correct if the triangle intersect at the very precise same coordinate - as the circles intersect. (…and as fas as I can tell after calculating on it - they do?)

Radius of circles and their centerpoints

$\displaystyle R_1 = 4, h_1, k_1 = [4,0]$

$\displaystyle R_2 = 2, h_2, k_2 = [8,2]$

triangle segment as function:

$\displaystyle y = x/2$

Circle formula and substitution with

$\displaystyle R_1 = (h_1-x)^2 + (k_1-y)^2$

$\displaystyle 16=(4-x)^2+(x/2)^2$

$\displaystyle => x=0 , x=32/5$

$\displaystyle R_2 = (h_1-x)^2 + (k_1-y)^2$

$\displaystyle 4=(8-x)^2 + (2-x/2)^2$

$\displaystyle => x=32/5 , x =8$

I added a diagram to with a symbolic interpretation rather than a color difference.

And, if an area had a resulting ++ or --, i.e 'double layers'

You'd had to calculate that area.