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

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Steve Gray

Posts: 103
Registered: 7/6/07
Null intersection of 3 circle interiors
Posted: Sep 10, 2007 3:28 PM
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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
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.

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