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equal angles wanted and given, square (2016 Kyiv City MO 9.5.1 10.4.1)

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September 5, 2020
geometryequal anglessquare

Problem Statement

On the sides ABAB and ADAD of the square ABCDABCD, the points NN and PP are selected, respectively, so that PN=NCPN = NC, the point QQ Is a point on the segment ANAN for which ∠NCB=∠QPN\angle NCB = \angle QPN. Prove that ∠BCQ=12∠PQA\angle BCQ = \tfrac {1} {2} \angle PQA.
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