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fighting circles

Source: Iran 3rd round 2011-final exam-p6

September 12, 2011
geometry proposedgeometry

Problem Statement

We call two circles in the space fighting if they are intersected or they are clipsed. Find a good necessary and sufficient condition for four distinct points A,B,A′,B′A,B,A',B' such that each circle passing through A,BA,B and each circle passing through A′,B′A',B' are fighting circles.
proposed by Ali Khezeli
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