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Concurrency in Parallelogram

Source: 2021 ISL G1

July 12, 2022
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Problem Statement

Let ABCDABCD be a parallelogram with AC=BC.AC=BC. A point PP is chosen on the extension of ray ABAB past B.B. The circumcircle of ACDACD meets the segment PDPD again at Q.Q. The circumcircle of triangle APQAPQ meets the segment PCPC at R.R. Prove that lines CD,AQ,BRCD,AQ,BR are concurrent.
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