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February 10th, 2013, 07:29 PM   #1
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A Geometry Problem I composed in 1992

Circa 1992 (Math Camp in preparation for a National Olympiad somewhere in Europe)

We're given a triangle ABC. Going clockwise, let B1 and B2 be distinct points inside the segment AC (B1 is between A and B2), let A1 and A2 be distinct points inside the segment CB (A1 is between C and A2), and finally let C1 and C2 be distinct points inside the segment AB (C1 is between B and C2).
The circumcircles of triangles CB1A1 and CB2A2 intersect at C3 != C. The circumcircles of triangles BA1C1 and BA2C2 intersect at B3 != B. The circum-circles of triangles AB1C1 and AB2C2 intersect at A3 != A.
Prove that the lines AA3, BB3 and CC3 have have a common point.
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February 26th, 2013, 04:17 PM   #2
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Re: A Geometry Problem I composed in 1992

I have an idea. How about drawing it to scale so we can SEE it? Since this is a "geometry" problem.
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