Distance from Circle to Line in 3-D

Date: 8/9/96 at 19:56:2
From: Ryan Bay
Subject: Distance from Circle to Line in 3-D

Dear Dr. Math,

What is the analytic formula for the nearest distance from a circle to 
a line or line segment in 3-space?  Also, what are the coordinates for 
the nearest points on the circle and line?

Thank you very much for your time.

     Yours,
       Ryan Bay
       Physics grad student

Date: 8/11/96 at 12:8:54
From: Doctor Anthony
Subject: Re: Distance from Circle to Line in 3-D

A circle in 3D will be defined as the surface of intersection of some 
conicoid (e.g. sphere or cone) with a plane.  If you then have the 
coordinates of the centre of the circle, you can next determine the 
equation of the plane containing the given line and the centre of the 
circle.  Where this plane cuts the circle is the point on the circle 
of nearest approach, and its distance from the given line is the 
shortest distance between the line and the circle.

There is no simple formula to give this information, since the circle 
in 3D cannot be expressed by some simple formula.

-Doctor Anthony,  The Math Forum
 Check out our web site!  http://mathforum.org/dr.math/