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KJMO 2000 P3 AD, BQ, CR meet at one point

Source: KJMO 2000

June 29, 2024
geometryKJMO

Problem Statement

Acute triangle ABCABC is inscribed in circle OO. PP is the foot of altitude from AA to BCBC, and DD is the intersection of OO and line APAP. M,NM, N are midpoint of AB,ACAB, AC respectively. MPMP and CDCD intersects at QQ, and NPNP and BDBD intersects at RR. Show that AD,BQ,CRAD, BQ, CR meet at one point if and only if AB=ACAB=AC.
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