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Height intersects circumcircle and 2 equal segments

Source: Iran second round- 2013- P3

May 4, 2013
geometrycircumcircletrapezoidparallelogramtrigonometrygeometric transformationreflection

Problem Statement

Let MM be the midpoint of (the smaller) arc BCBC in circumcircle of triangle ABCABC. Suppose that the altitude drawn from AA intersects the circle at NN. Draw two lines through circumcenter OO of ABCABC paralell to MBMB and MCMC, which intersect ABAB and ACAC at KK and LL, respectively. Prove that NK=NLNK=NL.
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