Re: intersection of two circles
- To: mathgroup at smc.vnet.net
- Subject: [mg105856] Re: intersection of two circles
- From: dh <dh at metrohm.com>
- Date: Tue, 22 Dec 2009 04:03:59 -0500 (EST)
- References: <hgno39$55l$1@smc.vnet.net>
Hi Felix,
assume the center of circle one is: p1={x1,y1}, that of circle two:
p2={x2,y2}. The radii are: r1 and r2. The intersections you are looking
for have a distance of r1 from p1 and r2 from p2:
p1 = {x1, y1};
p2 = {x2, y2};
p = {x, y};
eq = {
(p - p1).(p - p1) == r1^2,
(p - p2).(p - p2) == r2^2
};
Solve[eq, {x, y}]
Note that you will get two solutions.
If you solve this for general xi,yi, ri you get a fearsome formula, but
for numerical input the answer will be simple.
Daniel
Felix wrote:
> Hey,
> I m already hours busy with trying to find a way to indicate the coordinates of the point(s) where two circles intersect.
> Does Mathematica have a function that gives me the points of intersection if my input are the coordinates (in 2D) and the radii.
> Thanks,
>
> Felix
>