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60^o angle wanted, equilateral on a square

Source: 2019 Austrian Mathematical Olympiad Junior Regional Competition , Problem 2

December 18, 2020
geometryperpendicular bisector

Problem Statement

A square ABCDABCD is given. Over the side BCBC draw an equilateral triangle BCSBCS on the outside. The midpoint of the segment ASAS is NN and the midpoint of the side CDCD is HH. Prove that ∠NHC=60o\angle NHC = 60^o. . (Karl Czakler)
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