How to Construct a Circle With a Compass

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  • 0:04 What Is a Circle?
  • 0:46 What Is a Compass?
  • 1:09 Constructing a Circle
  • 2:22 Example 1
  • 3:08 Example 2
  • 4:00 Lesson Summary
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Lesson Transcript
Instructor: Michael Quist

Michael has taught college-level mathematics and sociology; high school math, history, science, and speech/drama; and has a doctorate in education.

Constructing a circle with a compass is easy to do, once you've mastered a few techniques. In this lesson, we'll explore an approach that gives great results, every time.

What Is a Circle?

It's funny the kinds of answers you get if you ask for the definition of a circle: ''It's a round thing -you know, like an orange or a ball!'' Everyone knows what a circle looks like, but not so many know how it is defined.

In math, a circle is defined as the set of points on a plane (a flat surface that is infinite in every direction) that are all the same distance from a given point. The given point is called the center of the circle. The same distance is called the radius. In circle construction, the center is where you put the metal point of the compass, the radius is how wide you set the two arms of the compass, and the circle is the curved line that you draw.

What Is a Compass?

A compass is an instrument, usually metal, that you can use to draw circles or arcs, and to measure distances for constructions in geometry. It has two adjustable arms, one with a pointed metal tip and the other with a small mounted pencil. Some compasses have controls for locking the width of the arms and locking the height of the pencil tip and metal point.

Constructing a Circle

All right, here are the steps for drawing a perfect circle:

  1. Locate and mark the place where you want the center of your circle.

  2. Determine the radius. It may be a measurement or a distance between other points on the drawing. Make sure you know exactly how long the radius should be.

  3. Put the compass point and pencil lead close to each other, and make sure they are set to roughly the same length. That will make the circle easier to draw. Tighten the grips on the pencil and compass point.

  4. Widen the arms of the compass to the radius you want, and tighten the hinge at the top (as in lock the arms).

  5. Re-measure your radius, just to make sure the compass arms did not slip.

  6. Place the metal point of the compass on the mark you made for the center of the circle.

  7. Pressing evenly on the metal point and pencil, turn the knob at the top of the compass, moving the pencil point all the way around the circle. If the circle is too light, do it again, pressing a little harder.

Now that we know how to construct a circle with a compass, let's take a look at a couple of examples: first constructing a circle on an existing drawing and then constructing a circle with a given measurement.

Example 1

Let's construct a circle with its center at the end of a line and the circle's edge touching another point. With this kind of project, you will use the distance on the drawing to set your compass width.

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