I am trying to calculate the touching point of two circles. I have the following information.
Circle $1$:
- Centre $(h,k)$
- Radius $r_1$
Circle $2$:
- Point on Circumference $(x_1,y_1)$
- Radius $r_2$
From this I would like to calculate the centre point of circle $2$: $(s,r)$ and the point where they touch: $(x,y)$.
I have worked out that to find the second centre point I can express the formulas like this:
$$(x_1-s)^2+(y_1-r)^2=r_2^2$$
$$(s-h)^2+(r-k)^2=(r_1+r_2)^2$$
Unforunately my maths skills are not up to the task of solving these equations for $s$ and $r$, and ultimately for $x$ and $y$.
I would appreciate any help that can be provided.
Regards
Martin.