Question 8
The triangle $ABC$ has area $1$. $D$, $E$, $F$ are the midpoints of the sides $BC$, $CA$, $AB$. $P$ lies in the segment $BF$, $Q$ lies in the segment $CD$, $R$ lies in the segment $AE$. What is the smallest possible area for the intersection of triangles $DEF$ and $PQR$?