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<DPA+ <AQD =< QIP wanted, incircle circumcircle related

Source: IMo 2019 SL G6

September 22, 2020
geometrycircumcircleIMO ShortlistIMO Shortlist 2019nice geo

Problem Statement

Let II be the incentre of acute-angled triangle ABCABC. Let the incircle meet BC,CABC, CA, and ABAB at D,ED, E, and F,F, respectively. Let line EFEF intersect the circumcircle of the triangle at PP and QQ, such that FF lies between EE and PP. Prove that ∠DPA+∠AQD=∠QIP\angle DPA + \angle AQD =\angle QIP.
(Slovakia)
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