Sides of Orthic Triangle of Obtuse Triangle

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

Let $\angle A$ be the obtuse angle of $\triangle ABC$.

Let $\triangle DEF$ be the orthic triangle of $\triangle ABC$.

Then the sides of $\triangle DEF$ are $-a \cos A$, $b \cos B$ and $c \cos C$.