Excenters and Incenter of Orthic Triangle/Acute Triangle

Theorem
Let $\triangle ABC$ be an acute triangle.

Let $\triangle DEF$ be the orthic triangle of $\triangle ABC$ such that:
 * $D$ is on $BC$
 * $E$ is on $AC$
 * $F$ is on $AB$

Then:
 * the excenter of $\triangle DEF$ $EF$ is $A$
 * the excenter of $\triangle DEF$ $DF$ is $B$
 * the excenter of $\triangle DEF$ $DE$ is $C$.

Proof

 * Excircle-of-Orthic-Triangle.png