Firstly, it's really hard to enter a "descriptive title" for this, but that's beside the point

Anyways, here's the problem I have:

If , and are altitudes of triangle , and and are points on and respectively such that , prove that bisects .

I've done substantial angle chasing with the orthic triangle, but I can't seem to prove that it is an angle bisector. I've used only 2 pronumerals for angles: for and for and I'm trying to prove is also . Is this the correct/ a good approach? If not, what'd be better? Some hints would do fine, all I've got atm is a huge bunch of angle chasing rubbish