RIOPLATENSE 2013 Problem 6

Let $ABC$ be an acute scalene triangle, $H$ its orthocenter and $G$ its geocenter. The circumference with diameter $AH$ cuts the circumcircle of $BHC$ in $A'$ ( $A' \neq H$ ). Points $B'$ and $C'$ are defined similarly. Show that the points $A'$ , $B'$ , $C'$ , and $G$ lie in one circumference.