Question 8
At an acute angle $\triangle ABC$ point $M$ is the center of the page $BC$, and points $D, E$ and $F$ are the bases of the heights from the vertex $A, B$ and $C$, respectively. Let it be $H$ orthocenter $\triangle ABC$, $S$ center longer $AH$, whereas $G$ section longer $FE$ and $AH$. If it is $N$ the point of intersection of the center of gravity of the length $AM$ and described circles $\triangle BCH$, prove that it is $\measuredangle HMA = \measuredangle GNS$.