Question

identify the fourth step in constructing a hexagon inscribed in a circle.

make an arc across the circle. this will be the next vertex of the hexagon.

set the compass on point a and set the width of the compass to the center of the circle. the compass is now set to the radius of the circle.

continue in this way until you have all six vertices.

draw a line between each of the successive pairs of vertices for a total of six lines.

Explanation:

To construct a regular hexagon inscribed in a circle, the typical steps are: 1. Set the compass to the radius (center to a point on the circle, say point A). 2. Make an arc from point A to get the next vertex. 3. Repeat to get more vertices. 4. After getting some vertices, continuing to create vertices until all six are formed (the fourth step involves continuing the process of creating vertices by repeating the arc - making, but among the options, "Continue in this way until you have all six vertices" aligns with the later steps after initial arc - making and setting the compass. Wait, no, let's re - order:

1. Set compass on center, width to radius (or on point A, width to center? Wait, standard step 1: Draw a circle, mark center O. Step 2: Place compass on a point A on the circle, width = OA (radius). Step 3: Make an arc across the circle to get point B (second vertex). Step 4: Place compass on B, make arc to get C (third vertex? No, wait, maybe the steps here are phrased differently. Let's analyze the options:

• Option 1: "Make an arc across the circle. This will be the next vertex of the hexagon." This is like step 2 or 3 (after setting compass).
• Option 2: "Set the compass on point A and set the width of the compass to the center of the circle. The compass is now set to the radius of the circle." This is step 1 (setting the compass to radius).
• Option 3: "Continue in this way until you have all six vertices." After making the first few arcs (vertices), the fourth step would be continuing to make arcs until all six are there.
• Option 4: "Draw a line between each of the successive pairs of vertices for a total of six lines." This is the last step, connecting the vertices.

So the fourth step is to continue making vertices (arcs) until all six are formed, which is the option "Continue in this way until you have all six vertices".

Answer:

The option "Continue in this way until you have all six vertices" (the third option in the list).