Question 93
Let $k$ be a circle with center $O$ and radius $\sqrt{5}$ and let $M$ and $N$ be points on a diameter of $k$ such that $MO = NO$. The chords $AB$ and $AC$, passing through $M$ and $N$, respectively, are such that
$$
\frac{1}{MB^{2}} + \frac{1}{NC^{2}} = \frac{3}{MN^{2}}
$$
Find the length of $MO$.
$$
\frac{1}{MB^{2}} + \frac{1}{NC^{2}} = \frac{3}{MN^{2}}
$$
Find the length of $MO$.