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 http://mathforum.org/dr.math/
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