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: Null intersection of 3 circle interiors
Replies: 2   Last Post: Sep 12, 2007 5:37 PM

Advanced Search

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

Posts: 102
Registered: 7/6/07
Null intersection of 3 circle interiors
Posted: Sep 10, 2007 3:28 PM
  Click to see the message monospaced in plain text Plain Text   Click to reply to this topic Reply

Place three points A,B,C in the plane, not in a line. Put
another point P strictly inside the triangle. Draw circles A,P,B;
B,P,C; and C,P,A. Show that these three circles have no interior
points in common, that is, their intersection is null (excluding the
circumferences).
This seems obvious but I need a geometric or algebraic proof
and don't have one. (If A,B,C,P is convex the circles do have interior
points in common.) Thank you for any hints or solutions.



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.