This content is licensed under Creative Commons Attribution/Share-Alike License 3.0 (Unported). That means you may freely redistribute or modify this content under the same license conditions and must attribute the original author by placing a hyperlink from your site to this work https://planetcalc.com/8098/. Also, please do not modify any references to the original work (if any) contained in this content.
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.
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):
|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:
Note the opposite signs before second addend