Question 16
On the base $BC$ of the isosceles triangle $ABC$ points $D$ and $E$ are chosen such that $BD = EC = 7$ cm. A line perpendicular to side $AB$ and passing through point $A$ intersects base $BC$ at point $F$. An altitude of triangle $ACE$ is $EG$, a median of triangle $AEF$ is $AH$. It is known that $\angle DAF = \frac{1}{2}\angle BAC$. Find the length of the segment $GH$.