Angles of Orthic Triangle of Obtuse Triangle/Proof

Proof

 * Orthic-Triangle-Obtuse.png

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

The quadrilateral $\Box DBEA$ is cyclic.

That is, $\Box DBEA$ can be circumscribed.

Hence:

Similarly, $\Box BEFC$ is also a cyclic quadrilateral.

Then:

The same argument can be applied to $C$, where we find:


 * $(4): \quad \angle EFD = 2 C$

Hence:

Hence the result.