In a triangle $ABC$, let $D$, $E$ and $F$ be the feet of the altitudes from $A$, $B$ and $C$ respectively. Let $D'$, $E'$ and $F'$ be the second intersection of lines $AD$, $BE$ and $CF$ with the circumcircle of $ABC$. Show that the triangles $DEF$ and $D'E'F'$ are similar.