Distance from Foot of Altitude of Triangle to Orthocenter

Theorem
Let $\triangle ABC$ be a triangle with sides $a$, $b$ and $c$ opposite vertices $A$, $B$ and $C$ respectively.

Let $D$ be the foot of the altitude of $\angle A$

Let $H$ be the orthocenter of $\triangle ABC$.

Then:
 * $HD = 2 R \cos B \cos C$