Question

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

Step 1: Use the straightedge to draw a diameter of the circle. Label the points at which the diameter touches the circle as A and B.
Step 2: Draw a second diameter through the center. Label the points at which the second diameter touches the circle as C and D.
Step 3: Join the end points of the two diameters to form a square.

What is the error in Lara's construction?

A. Show a diameter that did not pass through the center of the circle
B. She uses straightedge and not a compass to draw the diameter of the circle
C. She did not ensure that the second diameter was perpendicular to the first diameter
D. She did not ensure that the second diameter had the same length as the first diameter

Answer 1

The answer is C. You can make a rectangle by putting the diagonals through the center anywhere, but if you want a square, you have to put the two diagonals perpendicular to each other and join their ends. See the diagram.