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OX , BC concurrent with perp. bisector of AH, if XACH #, OH//BC

Source: 2022 IMOC G1 https://artofproblemsolving.com/community/c6h2918249p26069468

September 5, 2022
geometryCircumcenterorthocenterconcurrency

Problem Statement

The circumcenter and orthocenter of ABCABC are OO and HH, respectively. Let XACHXACH be a parallelogram. Show that if OHOH is parallel to BCBC, then OXOX and ABAB intersect at some point on the perpendicular bisector of AHAH.
proposed by USJL
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