# Where Do They Concur?

Geometry Level 3

Let $$\triangle ABC$$ be an acute triangle with circumcircle $$\omega.$$ $$D,E,F$$ are the feet of perpendiculars from $$A,B,C$$ to $$BC,CA,AB$$ respectively. Let $$\ell_A, \ell_b, \ell_C$$ be the lines passing through $$A,B,C$$ and parallel to $$BC,CA,AB$$ respectively. Let $$P,Q,R$$ be the second points of intersection (apart from $$A,B,C$$ respectively) of $$\ell_A, \ell_B, \ell_C$$ with $$\omega$$ respectively. It turns out that lines $$PD, QE, RF$$ concur at a point $$X$$ within $$\triangle ABC.$$ Then, $$X$$ is the ............ of $$\triangle ABC.$$

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