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OH parallel to BC

Source: 2022 Taiwan TST Round 2 Independent Study 2-G

April 8, 2022
geometry

Problem Statement

Let ABCABC be a triangle with circumcenter OO and orthocenter HH such that OHOH is parallel to BCBC. Let AHAH intersects again with the circumcircle of ABCABC at XX, and let XB,XCXB, XC intersect with OHOH at Y,ZY, Z, respectively. If the projections of Y,ZY,Z to AB,ACAB,AC are P,QP,Q, respectively, show that PQPQ bisects BCBC.
Proposed by usjl
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