Problem

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

Tags: geometry proposed, geometry



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 $A,B,A',B'$ such that each circle passing through $A,B$ and each circle passing through $A',B'$ are fighting circles. proposed by Ali Khezeli