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Angles and points on a square

Source: Iran National Olympiad - 2014 Second Round - D1P2

May 1, 2014
geometrygeometry proposed

Problem Statement

Let ABCDABCD be a square. Let N,PN,P be two points on sides AB,ADAB, AD, respectively such that NP=NCNP=NC, and let QQ be a point on ANAN such that ∠QPN=∠NCB\angle QPN = \angle NCB. Prove that ∠BCQ=12∠AQP. \angle BCQ = \dfrac{1}{2} \angle AQP .
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