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

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 Steve Gray Posts: 103 Registered: 7/6/07
Two problems on intersection of circles
Posted: Oct 5, 2007 10:58 AM

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.

Date Subject Author
10/5/07 Steve Gray
12/15/07 Steve Gray