MathNet 2021 — Part 04 Question 79

In triangle $A B C$, let $M$ be the midpoint of $B C$, $H$ be the orthocenter, and $O$ be the circumcenter. Let $N$ be the reflection of $M$ over $H$. Suppose that $O A = O N = 11$ and $O H = 7$. Compute $B C^{2}$.