Question

g is the center of the circle.
what will be the next step in constructing the perpendicular bisector of gj?
draw a circle with radius equal to ig and center h
draw a circle with radius equal to jh and center h
draw a circle with radius equal to ig and center j
draw a circle with radius equal to jh and center j

Explanation:

Step1: Recall perpendicular - bisector construction

To construct the perpendicular bisector of a line segment \(GJ\), we first need to find points that are equidistant from \(G\) and \(J\). After some initial steps (not shown here), we know that we can use circles to find such points.

Step2: Analyze the correct radius - center combination

We should draw circles with the same radius from the two endpoints of the line segment \(GJ\) (i.e., \(G\) and \(J\)). The radius should be more than half of the length of \(GJ\). If we consider the current state of the construction, we need to draw a circle with radius equal to \(IG\) (or \(JG\)) and center \(J\) to intersect with the other circle (drawn or to be drawn from \(G\)) to find the points that will help in constructing the perpendicular bisector.

Answer:

Draw a circle with radius equal to \(IG\) and center \(J\)