Problem

Source: 2023 USAJMO Problem 2/USAMO Problem 1

Tags: USAMO, USAJMO, USA(J)MO, geometry, xtimmyGgettingflamed



In an acute triangle $ABC$, let $M$ be the midpoint of $\overline{BC}$. Let $P$ be the foot of the perpendicular from $C$ to $AM$. Suppose that the circumcircle of triangle $ABP$ intersects line $BC$ at two distinct points $B$ and $Q$. Let $N$ be the midpoint of $\overline{AQ}$. Prove that $NB=NC$. Proposed by Holden Mui