Circles Self Teaching – Topic A: The Parts of a CircleIn this tutorial, we will learn how to identify the parts of a circle.

Section 1: What is the mathematical definition of a circle?

You’ve been able to identify a circle since you were only a few years old. But if you had to describe it mathematically, what would you say?

You might say something about how it’s perfectly round. A more complete definition would be that a circle is a group of points that are all the same distance away from another point.

For instance, this circle’s center is at point O. Point A is on the circle itself. The big idea of a circle, is that if we move A around the outside of the circle, it will always be exactly the same distance away from the center.

Section 2: Naming the parts of a circle.

Copy the sketch and the words in red in your notebook:

A radius (plural: radii) is a line segment that connects the center of the circle to the outside of the circle. Notice that all radii within a circle are the same length.

A diameter is a line segment that connects two points on the outside of the circle and passes through the center. The diameter of a circle is double the length of the radius.

A chord is a line segment that connects any two points on the outside of the circle. Question: Based on that definition, do you think a diameter is a chord?

The circumference of a circle is the distance around the outside of the circle. It’s identical to the idea of perimeter for other shapes.

Section 3: Practice

We name line segments by writing the two endpoints and putting a line above the letters. For instance segment MO is a radius, while QO is a _______________.

Name all the chords, radii, and diameters in circle M. (We name circles by their centers).

Hint: There are 4 chords, 2 diameters, and 4 radii. Some line segments will belong to more than one list!

Some questions to consider:

What do you think is the largest chord in a circle?

How many radii and diameters do you think there are in a circle?

Quiz Yourself!

http://www.proprofs.com/quiz-school/quizshow.php?title=parts--circle_2&q=3&next=y

Helpful images

(Don’t worry about the last 4)

Common Mistakes

1) Some people get confused about whether you have to double the radius or the diameter. Remember, the diameter is bigger. So the radius times two is the diamter.

2) Some people forget that a diameter is chord, but more specific. A chord is a segment with both endpoints on the circle. A diameter is a segment on both endpoints on the circle that also passes through the center.

Helpful Videos

Parts of a circle:http://www.virtualnerd.com/pre-algebra/perimeter-area-volume/circles/define-circles/circle-definition

https://www.khanacademy.org/math/basic-geo/basic-geo-area-and-perimeter/area-circumference-circle/v/parts-of-a-circle