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?3.

Answer 1

In Step 2, Lara did not ensure that the second diamter was perpendicualr to the first diameter she drew.

The correct steps should be:

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 perpendicular to the first diameter. 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.