# Orthic Triangle and Angle Bisector

• Apr 12th 2009, 07:11 PM
Myrc
Orthic Triangle and Angle Bisector
Firstly, it's really hard to enter a "descriptive title" for this, but that's beside the point (Giggle)

Anyways, here's the problem I have:

If $PP'$, $QQ'$ and $RR'$ are altitudes of triangle $PQR$, and $X$ and $Y$ are points on $P'R'$ and $Q'R'$ respectively such that $\angle XPY=\angle P'PR$, prove that $PX$ bisects $\angle R'XY$.

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: $\alpha$ for $\angle P'PR$ and $\theta$ for $\angle R'XP$ and I'm trying to prove $\angle PXY$ is also $\theta$. 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 (Doh)
• Apr 13th 2009, 03:32 AM
Myrc
Ah well, never mind, I finally found a solution (Rock)
The trick was finding the millions of cyclic quads (ok, slightly exaggerated...)

I can post my sol'n up here if anyone wants it, but otherwise, see ya guys later (Hi)