Question

determine if a circle is either completely inside, overlapping with, or completely outside another circler

Answer 1

I hope you're asking for circles with same centre.

Let the eq of one circle (S1) be x^2+y^2=a^2

And eq of another circle (S2) be x^2++y^2=b^2.

*If a^2 > b^2, then S1 will be lie outside the circle S2.

*If a^2 =/b^2, then S1 will overlap the circle S2.

*If a^2 < b^2, then S1 will be lie inside the circle S2.