Dissecting Triangles

In the diagram, we can see that $K$ is the midpoint of $\overline{GJ},$ and that $\overleftrightarrow{HK}$ is the perpendicular to $\overline{GJ}$ through $K.$ Therefore, $\overleftrightarrow{HK}$ is the perpendicular bisector of $\overline{GJ}.$

According to the Perpendicular Bisector Theorem, in a plane, if a point lies on the perpendicular bisector of a segment, then it is equidistant from the endpoints of the segment. In our case, $H,$ is the point on the perpendicular bisector and $G$ and $J$ are the endpoints. Therefore, according to the theorem, $HG=JH.$ $$\begin{array}{c}HG=JH\Rightarrow HG=9.2\end{array}$$ Let's see this on the diagram.