Question 151
Let $ABC$ be a triangle and $D$, $E$, $F$ points on the circumcircle of triangle $ABC$ so that $AD$, $BE$ and $CF$ are diameters of the circumcircle. The lines $AE$, $BF$ and $CD$ form a triangle $A'B'C'$. Prove that $\triangle ABC$ is similar to $\triangle A'B'C'$.