When constructing an inscribed regular hexagon and an inscribed equilateral triangle, the step that is the same is to set the compass width to the radius of the circle.
Here's a step-by-step explanation:
1. Start by drawing a circle with a center point.
2. Set your compass width to the radius of the circle.
3. Place the point of the compass on the center of the circle and draw an arc that intersects the circle in two places.
4. Without changing the compass width, place the compass point on one of the intersection points and draw another arc that intersects the circle.
5. Repeat this process, placing the compass point on the new intersection point and drawing arcs until you have six arcs that intersect the circle.
6. Connect every other arc along the circle. This will give you the vertices of the hexagon.
7. To construct an inscribed equilateral triangle, connect three adjacent vertices of the hexagon with straight lines. These lines will form the sides of the equilateral triangle.
So, to summarize, when constructing both an inscribed regular hexagon and an inscribed equilateral triangle, you need to set the compass width to the radius of the circle. This ensures that the arcs you draw intersect the circle accurately.