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prove that the rectangle is a square, double angle is given

Source: Danube 2015 Junior P4

September 8, 2018
geometryrectangleperpendicular bisectoranglessquare

Problem Statement

Let ABCDABCD be a rectangle with AB≥BCAB\ge BC Point MM is located on the side (AD)(AD), and the perpendicular bisector of [MC][MC] intersects the line BCBC at the point NN. Let Q=MN∪AB{Q} =MN\cup AB . Knowing that ∠MQA=2⋅∠BCQ\angle MQA= 2\cdot \angle BCQ , show that the quadrilateral ABCDABCD is a square.
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