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Part of the 10th XMO

Problems(1)

PK bisects BC if AP _|_ OH

Source: 10th XMO (China) p2 https://artofproblemsolving.com/community/c3192772_geometry_regional_china

4/18/2024
Given acute triangle △ABC\vartriangle ABC with orthocenter HH and circumcenter OO (O≠HO \ne H) . Let Γ\Gamma be the circumcircle of △BOC\vartriangle BOC . Segment OHOH untersects Γ\Gamma at point PP. Extension of AOAO intersects Γ\Gamma at point KK. If AP⊥OHAP \perp OH, prove that PKPK bisects BCBC. https://cdn.artofproblemsolving.com/attachments/a/b/267053569c41692f47d8f4faf2a31ebb4f4efd.png
geometrybisects segment