Intersection of chord with circle knowing the length and a point Let's take a circle with radius R, and center in O (0, 0). We take on this circle a point A with coordinates xA and yA.
We know that point A is one of the endings of a chord with length l.
Which is the easiest method to find the intersections points with circle B and C, knowing this information?
Basically I think that the following sistem has to be solved in x and y. 
\begin{matrix}
 l = \sqrt{(x_A - x)^2 + (y_A - y)^2}\\ 
 x^2 + y^2 = R^2& 
\end{matrix}
See my drawing bellow, too. It's just an example.

I will give special thanks for who will solve this problem. It's a project for computer science that I will make it open source, when  will it be finished.

And, the project is open source!
Sure, it's not finished but, it starts working.
Follow it on Github: https://github.com/IonicaBizau/circular-mirror
Thank you for @mixedmath's suggestion: "You are essentially asking how to find the intersection points of two circles, right?" (link)
A screen shot with the app:

Any suggestions are appreciated.
