Intersection of two circles
This online calculator finds the intersection points of two circles given the center point and radius of each circle. It also plots them on the graph.
To use the calculator, enter x and y coordinate of a center and radius of each circle.
A bit of theory can be found below the calculator.
Circles intersection
The task is relatively easy, but we should take into account the edge cases, so, we should start from calculating the cartesian distance d between two center points and checking for edge cases by comparing d with radiuses r1 and r2.
Here are the possible cases (distance between centers is shown in red):
Case  Description  Rule 

Trivial case: the circles are coincident (or it is the same circle)  
The circles are separate  
One circle is contained within the other  

Two intersection points  You have one or two intersection points if all rules for edge cases above are not applied 

One intersection point  Trivial case of two intersection points 
So, if it is not an edge case, to find the two intersection points, calculator uses the following formulas (mostly deduced with Pythagorean theorem), illustrated with the graph below:
First calculator finds the segment a
and then the segment h
To find point P3, calculator uses the following formula (in vector form):
And finally, to get pair of points in case of two points intersection, calculator uses these equations:
First point:
Second point:
Note the opposite signs before second addend
For more information, you can refer to CircleCircle Intersection and Circles and spheres
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