 Ellipse inside and tangental to a circle

A graphic of this problem is at:

http://dl.dropbox.com/u/13390614/Question3.jpg

The problem: 
Find the center of a non axis aligned ellipse, positioned inside of and tangental to a circle, with the ellipse's center collinear with a circle radial (A in the graphic).

Note the radial is not particularly important - the "nearest tangental point" could be specified instead.

Any insight would be appreciated.

Gary

 Ellipse inside and tangental to a circle
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A graphic of this problem is at:

http://dl.dropbox.com/u/13390614/Question3.jpg

The problem: 
Find the center of a non axis aligned ellipse, positioned inside of and tangental to a circle, with the ellipse's center collinear with a circle radial (A in the graphic).

Note the radial is not particularly important - the "nearest tangental point" could be specified instead.

Any insight would be appreciated.

Gary
