A convex hexagon $ABCDEF$ satisfies $|AB|=|BC|;|CD|=|DE|;|EF|=|FA|$. Prove that the lines containing the altitudes of the triangles $BCD$, $DEF$, $FAB$ starting, respectively, at the vertices $C, E, A$, intersect at a common point.
How can I use Ceva's theorem in order to prove this? Any hints,
Thanks