Simple Analytic Geom Question

[Robert Lewis]

On Nov 23, 2004, at 2:06 PM, Ted Hill wrote:

> 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.

   This seems to be pretty simple.  First assume that one circle is 
centered at the origin.  Let (x1, y1) be one of the desired points on 
this circle, of radius r, say.  Then the line from (0,0) to (x1,y1) is 
perpendicular to the line from (0,0) to the center of the other circle, 
say (cx2, cy2).  Let theta = angle formed by this line (0,0) to 
(cx2,cy2) and x-axis.  Then the answer is x1 = +- r sin(theta), y1 = -+ 
r cos(theta).  Note that the radius of the second circle is irrelevant.

   Then translate the answer if the first circle moves off  the origin.

Bob Lewis
Fordham University
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