Question 2
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. One nonofficial editorial point; manual essay grading.
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. One nonofficial editorial point; manual essay grading.