I'm looking for a bit of help with my project. At this point the context is a bit irrelevant, but I'm looking to find the intersection points of multiple circles.
There are $3$ circles, with the mid-point co-ordinates of $(0,0) , (2,4)$ , and $(4,0)$. Their radii are given in terms of an unknown variable '$a$'.
I have defined my 3 circles using the standard circle formula of $(x-h)^2 + (y-k)^2 = r^2$
Circle $A: x^2 + y^2 = (0.97 \times a)^2$
Circle $B: (x-2)^2 + (y-4)^2 = a^2$
Circle $C: (x-4)^2 + y^2 = (0.43 \times a)^2$
As an end result I would like the $6$ intersection points in Cartesian form, assuming that each circle intersects with each other circle $2$ times.
I have tried solving for 'a' but always end up with my answer in terms of both x and y and then get a bit lost as to where to go from there.
This is my first time seeking online help for project help before, so please be kind. Any advice or suggestions would be greatly appreciated.
Edit: Just to add some clarification, the fact that I'm working with a 3rd variable is what is throwing me off I think. Should the radii of these circles be known values, I would not have any issues with this solution.