Drexel dragonThe Math ForumDonate to the Math Forum



Search All of the Math Forum:

Views expressed in these public forums are not endorsed by Drexel University or The Math Forum.


Math Forum » Discussions » Math Topics » geometry.research.independent

Topic: Two problems on intersection of circles
Replies: 1   Last Post: Dec 15, 2007 11:37 AM

Advanced Search

Back to Topic List Back to Topic List Jump to Tree View Jump to Tree View   Messages: [ Previous | Next ]
Steve Gray

Posts: 101
Registered: 7/6/07
Two problems on intersection of circles
Posted: Oct 5, 2007 10:58 AM
  Click to see the message monospaced in plain text Plain Text   Click to reply to this topic Reply

Here's a complement to my previously posted problems.

1. Given n=4 points A,B,C,D in the plane in convex position, draw all
4 circles through them: ABC, ABD, ACD, and BCD. Prove that the
intersection of the interiors of these 4 circles is non-null.

2. Given n=5 points A,B,C,D,E in the plane in convex position, draw
all ten circles through them: ABC, .... ,CDE. Assume no two of these
circles are externally tangent. Prove that the intersection of the
interiors of these 10 circles is non-null.

3. Show that this does not hold for n>5.

Part 3 is trivial but I have no proof of 1 or 2.




Point your RSS reader here for a feed of the latest messages in this topic.

[Privacy Policy] [Terms of Use]

© Drexel University 1994-2014. All Rights Reserved.
The Math Forum is a research and educational enterprise of the Drexel University School of Education.