The Math Forum

Ask Dr. Math - Questions and Answers from our Archives
Associated Topics || Dr. Math Home || Search Dr. Math

Shared Points on Concentric Circles

Date: 03/11/2004 at 10:09:20
From: Caitlyn
Subject: Concentric Circles

Can two concentric circles share only a few points?  If they are
concentric and they have the same radius, they would share all of
their points, and if they don't have the same radius they will share
no points.  It seems like it's all or none.

Date: 03/11/2004 at 14:18:36
From: Doctor Douglas
Subject: Re: Concentric Circles

Hi Caitlyn.

Thanks for writing to the Math Forum.

Yes, if two circles share the same center and the same radius, they
will share all of their points (and therefore be the same circle). 
And concentric circles without the same radius will share no points.

However, there is a case in which concentric circles can share only a
few points.  Your two cases are true only if the two circles are also
coplanar (which is the usual assumed case).  Two concentric circles
that exist in a three-dimensional space could intersect in only a
couple of points, with most of the points on the circles not being
common to both circles.

- Doctor Douglas, The Math Forum 
Associated Topics:
High School Conic Sections/Circles
High School Higher-Dimensional Geometry

Search the Dr. Math Library:

Find items containing (put spaces between keywords):
Click only once for faster results:

[ Choose "whole words" when searching for a word like age.]

all keywords, in any order at least one, that exact phrase
parts of words whole words

Submit your own question to Dr. Math

[Privacy Policy] [Terms of Use]

Math Forum Home || Math Library || Quick Reference || Math Forum Search

Ask Dr. MathTM
© 1994- The Math Forum at NCTM. All rights reserved.