The diagram represents a plot of land, EFGH, which is to be used for an observatory.

1. Construct equal arcs from the vertex $H$ on both arms of the angle.

With centre $H$, draw an arc cutting $HE$ at $A$ and $HG$ at $B$.

2. Locate a point on the angle bisector and draw the bisector.

With centres $A$ and $B$ and the same radius, draw arcs to meet at $C$ inside $\angle EHG$. Join $H$ to $C$. The line $HC$ is the required angle bisector.

1. Construct two equal-radius arcs from $E$ and $F$ to locate points equidistant from $E$ and $F$.

Set the compass radius to more than half of $EF$. With centre $E$, draw arcs above and below $EF$. Using the same radius and centre $F$, draw arcs to cut the first pair of arcs at two points.

2. Draw the perpendicular bisector through the two arc intersection points.

Join the two points of intersection of the arcs with a straight line. This line is the perpendicular bisector of $EF$.

1. Identify and shade the region satisfying both distance conditions.

From part (b), the perpendicular bisector of $EF$ divides the plot into points nearer to $E$ and points nearer to $F$. Keep the side containing $E$.

From part (a), the angle bisector of $\angle EHG$ divides the points inside $\angle EHG$ into points nearer to $EH$ and points nearer to $GH$. Keep the side nearer to $GH$.

Shade the overlap of these two regions inside quadrilateral $EFGH$.