Simple Analytic Geom Question

[Ted Hill]

Hello,
 
This is a 2D problem in the x, y plane.
 
My inputs are:
 
circle radius (same for both circles A & B)
center point for circle A
center point for circle B
 
What I want to find are:
 
The corner points of the rectangle that satisfies the following:
 
The four points lie on the circles (2 on each circle, at opposite ends
of a diameter) such that
 
2 sides of the rectangle are parallel to the line that joins the center
points of the circles.
 
The other two sides of the rectangle are diameters of the circles.
 
I need to run this repeatedly as the mouse moves, so I am looking for a
fairly efficient way to calculate the four corners of my rectangle.
 
Thank you,
 
Ted Hill
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