spliting geomtries by intersection into separsted elemnts

 hi

im looking for a way creating some paten, mandala style, by finding the new geometries created by the intersecion between circles. 

i found the points of each intersect but im not sure how to split the circles in these points and conects them correctly into new geometries.

my final goal is to be able to control each type of geomtry and and choose a color for each kind of shape created, just like mandala.

in joined some screenshot to explain myself and also the script gh.

thanks!