Common chords of pairs of circles
Source: Sharygin contest 2008. The correspondence round. Problem 11
September 3, 2008
geometry proposedgeometry
Problem Statement
(A.Zaslavsky, 9--10) Given four points , , , . Any two circles such that one of them contains and , and the other one contains and , meet. Prove that common chords of all these pairs of circles pass through a fixed point.