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Some geometry

Source: St Petersburg Olympiad 2012, Grade 9, P3

September 29, 2017
geometry

Problem Statement

ABCDABCD is inscribed. Bisector of angle between diagonals intersect ABAB anc CDCD at XX and YY. M,NM,N are midpoints of AD,BCAD,BC. XM=YMXM=YM Prove, that XN=YNXN=YN.
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