Find intersection point of 3 circles so first of all, I just want to point out that I am a beginner, so cut me some slack.
As the title says I have 3 circles.
I know the coordinates of each center and the radius of each circle.
What I want to know is a formula that I can calculate the intersection point(points) with if any are present.
As the picture:
3 circles
Thank you for your help!!
 A: Generally you can represent circles with a center $(x_0,y_0)$ and a radius $r$ in the following form, using the pythagorean theorem: The points $(x,y)$ on this circle are exactly the points that satisfy
$$(x-x_0)^2 + (y-y_0)^2 = r^2$$
You can write down this equation for all three circles. By evaluating the difference between each pair of equations (note that $x^2$ and $y^2$ will cancel out), you get three lines that go throu the two intersection points of the corresponding pair of circles. Now you can just find the intersection of those lines.
A: Let each circle be defined by its centre $(x_i,y_i)$ and radius $r_i$.
The equation of a circle is given by $(x-x_i)^2+(y-y_i)^2=r^2_i$
So for two circles we have a pair of simultaneous equations:
They are: $x^2-2xx_1+x^2_1+y^2-2yy_1+y^2_1=r^2_1$
and $x^2-2xx_2+x^2_2+y^2-2yy_2+y^2_2=r^2_2$
Are you happy dealing with that? You find two points where the two circles intersect. Then test each one to see if it obeys the equation of the third.
A: Let (x1,y1) , (x2,y2) and (x3,y3) be the centres of three circles.
Assuming point of intersection(x,y) exists.

