Where Do They Concur?

Geometry Level 3

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

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