Proving that if the Simson line of a triangle goes through the orthocenter, then the pole must be at a vertex.

Question

I’ve already proven that if the Simson line goes through its pole then the pole is at a vertex. Similarly, I’ve proven that if it is perpendicular to one of its sides then the pole must again be at a vertex. How can I prove this for when it goes through the orthocenter? Thanks in advance