It is easy to prove RSQP is cyclic; so that this can be easily shown in many ways.
e.g.
Let angle AQS = @; .: angle QBS = @; .: angle PRS = @ (PR // QB)
.: angle AQS = angle PRS
.: external angle AQS of quadrilateral RSQP = int opp angle PRS
.: RSQP must be cyclic
QED
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