Session 3: Construction of Circles – Steps, Interactives and Examples

Construction is similar to a drawing in that it produces a visual outcome. However, while drawings are often just rough sketches that help to convey an idea, constructions are step-by-step processes used to create geometric figures. To create a construction by hand, there are a few tools that you can use:

1. Compass: A device that allows you to create a circle with a given radius. Not only can compasses help you to create circles, but also they can help you to copy distances. 
2. Straightedge: Anything that allows you to produce a straight line. A straightedge is not used to measure distances when creating constructions. An index card works well as a straightedge. You can also use a ruler as a straightedge, as long as you only use it to draw straight lines and not to measure. 
3. Paper: When a geometric figure is on a piece of paper, the paper itself can be folded in order to construct new lines. 

What is a Circle?

A circle is a simple closed curve, with a set of all points at a constant distance from a fixed (centre) point, A,  in the same plane. Since the circle has only one centre, you can name the circle by naming its centre. In this way, you can name this circle A.

The distance from the centre point to the circle is called the radius (r).  In other words, a line segment joining the centre of a circle with any point on the circle is called a radius (plural: radii) of that circle. AB  is a radius of circle A.

The distance from one side of the circle to the other through the centre point is called the diameter (d).  In other words, a line segment joining any two points on a circle and passing through the centre of the circle is called a diameter of that circle. The diameter of a circle is twice its radius. PQ is the diameter of circleA.

Construct a Circle of a Given Radius

To construct a circle with a radius of 3 cm, we follow the following steps of construction:

Step 1: Place the metal point of the compass at the zero mark on the ruler and adjust the width of the compass such that the pencil point is at the mark 3 cm.

Step 2: Mark a point A on the paper. This point will be the centre of the circle.

Step 3: Place the metal point of the compass at point A.

Step 4: Press down the metal point and turn the knob at the top of the compass to construct the circle .

Construction of Circle – Examples

Example 1

Use your compass to construct a circle like the one shown below on a piece of paper. Describe how to fold the paper two times in order to help you construct a square.

Fold the circle so that the two halves overlap to create a crease that is the diameter.

Fold the circle in half again to create the perpendicular bisector of the diameter. To do this, fold so that the two endpoints of the diameter meet. The second crease will also be a diameter.

Note that the two diameters are perpendicular to one another. Connect the four points of intersection on the circle to construct a square.

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