Question 3
Let $ABC$ be an acute scalene triangle with altitudes $AD,BE,CF$. From $A$, drop perpendiculars to the lines $EF,FD,DE$, with feet $X,Y,Z$, respectively. Let the line $BZ$ meet the circle $(BDY)$ again at $P$, and let $CY$ meet $(CDZ)$ again at $Q$. Prove that $X$ has equal powers with respect to the circles $(YFP)$ and $(ZEQ)$.