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Japan MO Finals 2020-2

Source: Japan MO Finals 2020-2

February 12, 2020
Japangeometrycircumcircle

Problem Statement

Triangle ABCABC satisfies BC<ABBC<AB and BC<ACBC<AC. Points D,ED,E lie on segments AB,ACAB,AC respectively, satisfying BD=CE=BCBD=CE=BC. Lines BEBE and CDCD meet at point PP, circumcircles of triangle ABEABE and ACDACD meet at point QQ other than AA. Prove that lines PQPQ and BCBC are perpendicular.
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