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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
```

```
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/
```
Associated Topics:
College Higher-Dimensional Geometry

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