11

Part of 2008 Sharygin Geometry Olympiad

Problems(1)

Common chords of pairs of circles

Source: Sharygin contest 2008. The correspondence round. Problem 11

(A.Zaslavsky, 9--10) Given four points

A

B

C

D

. Any two circles such that one of them contains

A

B

, and the other one contains

C

D

, meet. Prove that common chords of all these pairs of circles pass through a fixed point.

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