Question 117
Consider triangle $ABC$ inscribed in circle $\omega$, and an interior point $P$. Lines $AP, BP$ and $CP$ intersect the circle $\omega$ for the second time at points $D, E, F$, respectively. Let $A', B', C'$ be the reflections of $A, B, C$ in the lines $EF, FD, DE$ respectively. Show that triangle $A'B'C'$ is similar to $ABC$.