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IMOC 2020 G5 concyclic wanted, parallelogram and concurrent related

Source: https://artofproblemsolving.com/community/c6h2254883p17398793

September 1, 2020
geometryparallelogramConcyclicconcurrent

Problem Statement

Let O,HO, H be the circumcentor and the orthocenter of a scalene triangle ABCABC. Let PP be the reflection of AA w.r.t. OHOH, and QQ is a point on ⊙(ABC)\odot (ABC) such that AQ,OH,BCAQ, OH, BC are concurrent. Let A′A' be a points such that ABA′CABA'C is a parallelogram. Show that A′,H,P,QA', H, P, Q are concylic.
(ltf0501).
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