Have a graph at desmos, but an unable to make the circles always intersect each other.
Request the missing logic (in the form of condition) that would enforce the two circles to always intersect only.
Edit Have implemented comment by @fleablood at https://www.desmos.com/calculator/7xmcap1o6r, but seems ineffective. May be my implementation is wrong.
You are not having a mathematical problem but rather a how to use desmos problem.
$$|r_1-r_2| \le \|P_1-P_2\|_2\le r_1+r_2$$
should be the right constraint but note that typing a constraint in a single entry does not impose any constraint on the curves.
This is a modification of your code such that the circles are only plotted when they intersect.