Let I be the incentre of acute-angled triangle ABC. Let the incircle meet BC,CA, and AB at D,E, and F, respectively. Let line EF intersect the circumcircle of the triangle at P and Q, such that F lies between E and P. Prove that ∠DPA+∠AQD=∠QIP.(Slovakia) geometrycircumcircleIMO ShortlistIMO Shortlist 2019nice geo