; This is a simple example of eliminate command usage.
; Combine the equations for 2 circles on a 2D Cartesian plane
; to find the points of intersection (x, y).

(x-x1)^2+(y-y1)^2=r1^2 ; circle of radius r1 with center at (x1, y1)
(x-x2)^2+(y-y2)^2=r2^2 ; circle of radius r2 with center at (x2, y2)
eliminate x ; combine the two equations, removing the x variable from the result
y ; solve for y
simplify
simplify