Question 108
In triangle $ABC$, $O$ is the circumcenter and $H$ is the orthocenter. $M$ and $N$ are the midpoints of $BH$ and $CH$ respectively and $BB'$ is a diameter of the circumcircle. If $HONM$ be an inscribed quadrilateral, prove that
$$
B'N = \frac{1}{2}AC
$$
$$
B'N = \frac{1}{2}AC
$$