How to perform non-linear optimization with scipy/numpy or sympy?

Question

I am trying to find the optimal solution to the follow system of equations in Python:

(x-x1)^2 + (y-y1)^2 - r1^2 = 0
(x-x2)^2 + (y-y2)^2 - r2^2 = 0
(x-x3)^2 + (y         


        

Answer 1

These equations can be seen as describing all the points on the circumference of three circles in 2D space. The solution would be the points where the circles intercept.

The sum of their radii of the circles is smaller than the distances between their centres, so the circles don't overlap. I've plotted the circles to scale below:

There are no points that satisfy this system of equations.