Question 130
In triangle $ABC$, the incenter is $I$ and the incircle touches the sides $BC, AC, AB$ at $D, E, F$, respectively. For a line $\ell$ passing through $I$, the feet of the perpendiculars dropped from $A, B, C$ onto $\ell$ are $X, Y, Z$ respectively. Show that the lines $DX, EY, FZ$ are concurrent.