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square construction given 4 collinear (2016 Kyiv City MO Round2 10.2 11.2 )

Source:

September 7, 2020
geometrycollinearconstructionsquare

Problem Statement

On the horizontal line from left to right are the points P,  Q,  R,  SP, \, \, Q, \, \, R, \, \, S. Construct a square ABCDABCD, for which on the line ADAD lies lies the point PP, on the line BCBC lies the point QQ, on the line ABAB lies the point RR, on the line CDCD lies the point SS .
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