# The Perpendiculars

Geometry Level 4

In acute $$\triangle ABC,$$ $$D, E, F$$ are the feet of perpendiculars from $$A, B, C$$ to $$BC, CA, AB$$ respectively. Let $$P, Q, R$$ be the feet of perpendiculars from $$A, B, C$$ to $$EF, FD, DE$$ respectively. It turns out that lines $$AP, BQ, CR$$ are concurrent at a point $$X$$ within $$\triangle ABC.$$ Then, $$X$$ is the:

Details and assumptions

• This problem is not original; I got this from one of my friends. I don't know its original source.
×