Problem

Source: Kazakhstan Junior MO 2023 9.1

Tags: geometry



The $C$-excircle of a triangle $ABC$ touches $AB, AC, BC$ at $M, N, K$. The points $P, Q$ lie on $NK$ so that $AN=AP, BK=BQ$. Prove that the circumradius of $\triangle MPQ$ is equal to the inradius of $\triangle ABC$.