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IGO-Intermediate-Problem 1

Source:

September 22, 2015
geometry proposedgeometry

Problem Statement

Given a circle and Points P,B,AP,B,A on it.Point QQ is Interior of this circle such that: 1)1) ∠PAQ=90\angle PAQ=90. 2)PQ=BQ 2)PQ=BQ. Prove that ∠AQB−∠PQA=AB⌢\angle AQB - \angle PQA=\stackrel{\frown}{AB}.
proposed by Davoud Vakili, Iran.
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