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angle chasing inside a square (Kharkiv City X 2014 - Ukr)

Source:

March 14, 2020
squareanglesAngle Chasingequal anglesKharkivgeometry

Problem Statement

Let ABCDABCD be a square. The points NN and PP are chosen on the sides ABAB and ADAD respectively, such that NP=NCNP=NC. The point QQ on the segment ANAN is such that that ∠QPN=∠NCB\angle QPN=\angle NCB. Prove that ∠BCQ=12∠AQP\angle BCQ=\frac{1}{2}\angle AQP.
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