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Circumcircle of NKL passes through midpoint of BC

Source: Greece MO 1999

May 27, 2011
geometrycircumcirclegeometry proposed

Problem Statement

In an acute-angled triangle ABCABC, AD,BEAD,BE and CFCF are the altitudes and HH the orthocentre. Lines EFEF and BCBC meet at NN. The line passing through DD and parallel to FEFE meets lines ABAB and ACAC at KK and LL, respectively. Prove that the circumcircle of the triangle NKLNKL bisects the side BCBC.
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