Question 161
The point $M$ is chosen inside of the convex quadrilateral $ABCD$ such that $\angle BMC = \angle AMD$. The triangles $ABE$ and $CDF$ are erected outwardly on the sides $AB$, $CD$ of the quadrilateral $ABCD$ such that
$$
\angle BAE = \angle DAM, \quad \angle ABE = \angle CBM, \quad \angle CDF = \angle ADM, \quad \angle DCF = \angle BCM.
$$
Prove that the points $M$, $E$, $F$ are collinear.
$$
\angle BAE = \angle DAM, \quad \angle ABE = \angle CBM, \quad \angle CDF = \angle ADM, \quad \angle DCF = \angle BCM.
$$
Prove that the points $M$, $E$, $F$ are collinear.