Question

Larry wants to inscribe an equilateral triangle 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: Set the width of the compass to the diameter of the circle.
Step 2: Plot a point on the circle. Place the compass on this point and draw two arcs to cut the circle. These two points of intersection between the arcs and the circle represent two of the vertices.
Step 3: Draw a segment between the two vertices. Adjust the width of the compass to the length of the segment. Place the compass on one vertex and draw an arc to construct the third vertex.
Step 4: Draw a line from one vertex to the next to form an equilateral triangle.

What is the error in Larry's construction?

A. He did not draw a pair of perpendicular bisectors to construct two diameters of the circle.
B. He drew only two arcs.
C. He set the width of the compass to the diameter of the circle.
D. He did not ensure that the length of the sides of the triangle was the same as the diameter of the triangle.

Answer 1

The error in Larry's construction is:

C. He set the width of the compass to the diameter of the circle.

Explanation:

The steps for the construction of an inscribed equilateral triangle is as follows:

• Step 1: Draw a circle on a piece of paper.Take a point anywhere on the circumference of the circle and take that point as a starting point.

• Step 2: Now without changing the span of the circle we have draw two arcs to cut the circle.These two points of intersection between the arcs and the circle represent two of the vertices.

• Step 3: Draw a segment between the two vertices. Adjust the width of the compass to the length of the segment. Place the compass on one vertex and draw an arc to construct the third vertex.

• Step 4: Draw a line from one vertex to the next to form an equilateral triangle.

Hence, the error he that he set the width of compass equal to the diameter of circle.

Instead he should have set the width of the compass equal to the radius of the circle.

Answer 2

Answer: The error in Larry's construction is Option C.

He set the width of the compass to the diameter of the circle. The step 1 should be: Set the width of the compass to the radius of the circle.