MathDB
Angle chasing problem

Source: Switzerland Final Round 2021 P2

February 24, 2021
geometry

Problem Statement

Let △ABC\triangle ABC be an acute triangle with AB=ACAB =AC and let DD be a point on the side BCBC. The circle with centre DD passing through CC intersects ⊙(ABD)\odot(ABD) at points PP and QQ, where QQ is the point closer to BB. The line BQBQ intersects ADAD and ACAC at points XX and YY respectively. Prove that quadrilateral PDXYPDXY is cyclic.
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