MathDB
IZhO 2010 1-st round-2

Source:

September 4, 2010
geometrycircumcirclecyclic quadrilateralgeometry proposed

Problem Statement

In a cyclic quadrilateral ABCDABCD with AB=ADAB=AD points MM,NN lie on the sides BCBC and CDCD respectively so that MN=BM+DNMN=BM+DN . Lines AMAM and ANAN meet the circumcircle of ABCDABCD again at points PP and QQ respectively. Prove that the orthocenter of the triangle APQAPQ lies on the segment MNMN .
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