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IMO Shortlist 2011, G7

Source: IMO Shortlist 2011, G7

July 13, 2012
geometrycircumcircleIMO Shortlist

Problem Statement

Let ABCDEFABCDEF be a convex hexagon all of whose sides are tangent to a circle ω\omega with centre OO. Suppose that the circumcircle of triangle ACEACE is concentric with ω\omega. Let JJ be the foot of the perpendicular from BB to CDCD. Suppose that the perpendicular from BB to DFDF intersects the line EOEO at a point KK. Let LL be the foot of the perpendicular from KK to DEDE. Prove that DJ=DLDJ=DL.
Proposed by Japan
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