Question 166
The isosceles triangle $ABE$, with $m(\angle ABE) = 120^\circ$, is constructed outside the square $ABCD$. Denote by $M$ the orthogonal projection of $B$ onto the bisector of angle $EAB$, by $N$ the orthogonal projection of $M$ onto $AB$ and by $P$ the meeting point of the straight lines $CN$ and $MB$. Let $G$ be the centroid of triangle $ABE$. Prove that the straight lines $PG$ and $AE$ are parallel.