To use the calculator, enter the x and y coordinates of a center and radius of each circle.
A bit of theory can be found below the calculator.
The task is relatively easy, but we should take into account the edge cases – therefore we should start by 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):
|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 the 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, the calculator uses the following formulas (mostly deduced with Pythagorean theorem), illustrated with the graph below:
The first calculator finds the segment a
and then the segment h
To find point P3, the calculator uses the following formula (in vector form):
And finally, to get a pair of points in case of two points intersecting, the calculator uses these equations:
Note the opposite signs before the second addend