Question 77
Let $C$, $E$ and $A$ be points on the sides $XY$, $YZ$ and $ZX$ of the triangle $XYZ$ respectively. Points $B$, $D$ and $F$ are chosen on the segments $AX$, $CY$ and $EZ$ respectively, so that $BC \perp AD$, $DE \perp CF$, $AF \perp BE$. Can it happen that the lines $XF$, $YB$ and $ZD$ are concurrent?