Looks like a quadratic equation to me, I'll try to code it out.
All done, here ya go. It'll show the two intersections of the circles.
sync on
cx1 = 400
cy1 = 300
r1 = 50
r2 = 75
DO
cls
cx2 = mousex()
cy2 = mousey()
ink rgb(255,255,255),0
circle cx2, cy2, r2
circle cx1, cy1, r1
d2# = (cx2-cx1)^2 + (cy2-cy1)^2
d# = sqrt(d2#)
if d# > r1+r2 then print "no solutions"
if d# < abs(r1-r2) then print "no solutions: circle is contained within the other"
if d# = 0 and r1 = r2 then print "infinite solutions: circles overlap"
x = ((cx2 + cx1)/2) + ((cx2-cx1)*(r1^2 - r2^2))/(2*d2#)
y = ((cy2 + cy1)/2) + ((cy2-cy1)*(r1^2 - r2^2))/(2*d2#)
px = ((cy2-cy1)/(2*d2#)) * sqrt(((r1+r2)^2 - d2#)*(d2#-(r2-r1)^2))
px1 = x + px
px2 = x - px
py = ((cx2-cx1)/(2*d2#)) * sqrt(((r1+r2)^2 - d2#)*(d2#-(r2-r1)^2))
py1 = y - py
py2 = y + py
ink rgb(255,0,0),0
circle px1, py1, 5
circle px2, py2, 5
set cursor 0,20
print x
print y
sync
LOOP
