Sam wants to inscribe a square in a circle using only a compass and straightedge.
He will first construct a circle and locate its center. He will then perform the following steps.

Step 1: Use the straightedge to draw a diameter of the circle.
Step 2: Copy the length of the diameter and construct another diameter.
Step 3: Join the points of intersection of the endpoints of the diameters and the circle.

What is the error in Sam’s steps?

Question

Sam wants to inscribe a square in a circle using only a compass and straightedge.
He will first construct a circle and locate its center. He will then perform the following steps.
 
Step 1: Use the straightedge to draw a diameter of the circle.
Step 2: Copy the length of the diameter and construct another diameter.
Step 3: Join the points of intersection of the endpoints of the diameters and the circle.
 
What is the error in Sam’s steps?

anonymous · Answer

He constructed only two diameters and not four.
		
He constructed two diameters of the same length.
		
He did not ensure that the diameters are at right angles to each other.
		
He did not ensure that the diameter passes through the center of the circle.