Question

using a compass and straight edge, construct a square inscribed in a circle.

which of the steps listed below and on the right did you include in your construction?

• i drew a circle with diameter \\(aob\\).
• i constructed two arcs with center at \\(a\\) or \\(b\\).
• i marked the points where the arc intersected the circle.
• i drew a segment connecting these points of intersection.
• i constructed an arc with center at the intersection of this segment and the diameter.
• i marked the points where the arc intersected the segment.
• i drew in a diameter through each of these points of intersection.
• i connected the points where these diameters intersected the circle to form a square.

Explanation:

Analyze the standard construction of an inscribed square

1. Draw a circle with center \(O\) and a diameter \(AOB\).
2. Construct the perpendicular bisector of diameter \(AOB\) by drawing arcs centered at \(A\) and \(B\) with a radius greater than the circle's radius.
3. Mark the intersection points of these arcs and draw a line (segment) through them, which is the perpendicular bisector.
4. Mark the points where this perpendicular bisector intersects the circle (let's call them \(C\) and \(D\)).
5. Connect the four points on the circle (\(A\), \(C\), \(B\), and \(D\)) sequentially to form the inscribed square.

Evaluate the given checklist options against the standard construction

• "I drew a circle with diameter AOB." -> Yes, this is the starting step.
• "I constructed two arcs with center at A or B." -> Yes, these are used to construct the perpendicular bisector of \(AOB\).
• "I marked the points where the arc intersected the circle." -> No, the arcs for the perpendicular bisector intersect each other outside the circle, not the circle itself.
• "I drew a segment connecting these points of intersection." -> Yes, connecting the arc intersections creates the perpendicular bisector.
• "I constructed an arc with center at the intersection of this segment and the diameter." -> No, the intersection is the center \(O\), and we do not need to draw another arc from \(O\).
• "I marked the points where the arc intersected the segment." -> No, this is not part of the standard square construction.
• "I drew in a diameter through each of these points of intersection." -> No, we only need the perpendicular bisector, which is already a diameter.
• "I connected the points where these diameters intersected the circle to form a square." -> Yes, connecting the four intersection points on the circle forms the square.

Select the correct steps

The correct steps included in the construction are:

1. I drew a circle with diameter \(AOB\).
2. I constructed two arcs with center at \(A\) or \(B\).
3. I drew a segment connecting these points of intersection.
4. I connected the points where these diameters intersected the circle to form a square.

Answer:

• I drew a circle with diameter AOB. (Correct answer)
• I constructed two arcs with center at A or B. (Correct answer)
• I marked the points where the arc intersected the circle.
• I drew a segment connecting these points of intersection. (Correct answer)
• I constructed an arc with center at the intersection of this segment and the diameter.
• I marked the points where the arc intersected the segment.
• I drew in a diameter through each of these points of intersection.
• I connected the points where these diameters intersected the circle to form a square. (Correct answer)