OMCPLP 2024 Problem 3

Day 1

Seja $ABC$ um triângulo cuja circunferência inscrita tem centro $I$ . Uma reta $r$ que passa por $I$ interseta as circunferências circunscritas aos triângulos $AIB$ e $AIC$ nos pontos $P$ e $Q$ , respetivamente. Prove que o circuncentro do triângulo $APQ$ pertence à circunferência circunscrita ao triângulo $ABC$ .

Official text Lusophon Mathematical Olympiad 2024 official paper, page 1. Quoted with source.

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