
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 nonnull.
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 nonnull.
3. Show that this does not hold for n>5.
Part 3 is trivial but I have no proof of 1 or 2.

