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Prove that chords are equal

Source: Argentina IMO TST 2006 problem 3

August 27, 2009
geometrytrapezoidangle bisectorgeometry unsolved

Problem Statement

In a circumference with center O O we draw two equal chord AB\equal{}CD and if AB \cap CD \equal{}L then AL>BL AL>BL and DL>CL DL>CL We consider M∈AL M \in AL and N∈DL N \in DL such that \widehat {ALC} \equal{}2 \widehat {MON} Prove that the chord determined by extending MN MN has the same as length as both AB AB and CD CD
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