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MPQ=2KML - Iran NMO 1997 (Second Round) - Problem2

Source:

October 5, 2010
geometrycircumcircle

Problem Statement

Let segments KN,KLKN,KL be tangent to circle CC at points N,LN,L, respectively. MM is a point on the extension of the segment KNKN and PP is the other meet point of the circle CC and the circumcircle of △KLM\triangle KLM. QQ is on MLML such that NQNQ is perpendicular to MLML. Prove that ∠MPQ=2∠KML. \angle MPQ=2\angle KML.
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