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Japan MO Finals 2021 P3

Source: Japan MO Finals 2021 P3

February 14, 2021
geometryJapan

Problem Statement

Points D,ED,E on the side AB,ACAB,AC of an acute-angled triangle ABCABC respectively satisfy BD=CEBD=CE. Furthermore, points PP on the segmet DEDE and QQ on the arc BCBC of the circle ABCABC not containing AA satisfy BP:PC=EQ:QDBP:PC=EQ:QD. Points A,B,C,D,E,P,QA,B,C,D,E,P,Q are pairwise distinct. Prove that ∠BPC=∠BAC+∠EQD\angle BPC=\angle BAC+\angle EQD holds.
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