Math resources Geometry

Circle math

Parts of a circle

# Parts of a circle

Here you will learn about the different parts of a circle including how to identify the key parts of a circle from a diagram, how to identify the key parts of a circle from a definition and how to draw a circle with the different parts labeled, such as the diameter of a circle.

Students will first learn about parts of a circle as part of geometry in high school.

## What are the parts of a circle?

The parts of a circle are the circle, center, radius, diameter, circumference, arc, area, chord, secant, tangent, sector and segment.

The definition of a circle is a closed plane figure where all points in a plane are equidistant, (the radius), from a given point (the center).

## Common Core State Standards

How does this relate to high school math?

• High School: Geometry (HS.G.CO.A.1)
Know precise definitions of angle, circle, perpendicular line, parallel line, and line segment, based on the undefined notions of point, line, distance along a line, and distance around a circular arc.

• High School: Geometry (HS.G.C.A.2)
Identify and describe relationships among inscribed angles, radii, and chords. Include the relationship between central, inscribed, and circumscribed angles; inscribed angles on a diameter are right angles; the radius of a circle is perpendicular to the tangent where the radius intersects the circle.

## How to identify parts of a circle

In order to identify and label parts of a circle:

1. Identify the key aspects of the part of the circle.

## Parts of a circle examples

### Example 1: identifying a part of a circle from a diagram

Name the part of the circle shown in blue in the diagram below.

1. Identify the key aspects of the part of the circle.

Here are some key questions you can ask yourself:

• Is it a line or part of the circle’s area? \hspace{2.75cm} Line
• If a line, does it go through the origin of the circle? \hspace{1cm} Yes
• If a line, is it part of the circle’s circumference? \hspace{1.6cm} No

The part of the circle shown in the diagram is the radius.

### Example 2: identifying a part of a circle from a diagram

Name the part of the circle shown in yellow in the diagram below.

Identify the key aspects of the part of the circle.

### Example 3: identifying a part of a circle from a diagram

Name the part of the circle shown in blue in the diagram below.

Identify the key aspects of the part of the circle.

### Example 4: identifying a part of a circle from a diagram

Name the part of the circle shown in yellow in the diagram below.

Identify the key aspects of the part of the circle.

### Example 5: identifying a part of a circle from a diagram

Name the part of the circle shown in blue in the diagram below.

Identify the key aspects of the part of the circle.

### Example 6: labeling a part of a circle on a diagram

On the circle below:

Draw a diameter

Draw a tangent

Label the circumference

Identify the key aspects of the part of the circle.

### Teaching tips for parts of a circle

• Instead of relying on worksheets for students to identify the parts of the circle, consider interactive activities for student practice. Provide students with real-world examples and have them measure the diameter and find the longest chord on that example.

• Use technology to allow students to interact with circles in a different way. There are many educational apps and interactive websites that offer simulations and exercises that lead to deeper understanding.

### Easy mistakes to make

• Confusing the radius and the diameter
The radius is from the center of the circle to the circumference while the diameter goes across the whole circle. Both will pass through the origin.

• Confusing the segment and the sector
A segment is made from a chord while a sector will have lines (radii) coming from the origin.
Note: Some students like to consider a sector like a slice of pizza.

• Confusing the chord and the diameter
A chord of the circle will not go through the origin of the circle while the diameter will.

• Confusing the tangent and the secant
A tangent only touches the circumference at a single point, it does not cross the line. A secant will cross the circumference twice.

### Practice parts of a circle questions

1. If a circle has an ‘O’ noted on it, it normally notes the:

Circle is an O shape

Middle of the circle (origin)

Name of the circle is O

A circle inside a circle

The ‘O’ refers to the center of the circle which is called the origin of the circle.

2. Which will be the longest in length of any circle?

Diameter

Chord

Circumference

The circumference is the distance around the edge of the circle, this will always be longer than the radius, diameter or a chord.

3. What part of the circle is shown in the diagram below?

a secant

a sector

a tangent

a segment

The secant of a circle is a line that goes through the circle at two points.

4. A line that touches the circumference of a circle at one point is called a:

A secant

A segment

A tangent

An arc

A tangent is a straight line that touches the circle at a single point only.

5. Which of the following statements is true?

The radius is twice the length of the diameter:

The diameter is twice the length of the radius.

The radius is half the length of the circumference.

The diameter is half the length of the circumference.

The diameter is twice the length of the radius. The distance from the center of the circle to the circumference is called the radius.

The distance across the circle passing through the center is called the diameter. This means that the diameter is twice as long as the radius.

6. A sector is:

Part of a circle’s circumference

Part of a circle’s area

A line that goes through a circle

The middle of a circle

A sector consists of the area created by an arc and two radii.

## Parts of a circle FAQs

What is the radius of a circle?

The radius of a circle is the distance from the center to any point on the circle’s circumference. It is typically represented by an r.

What are concentric circles?

Concentric circles are circles that share the same center but have a different radius. They are often circles that are nested within one another.

A cyclic quadrilateral is a quadrilateral whose vertices are located on the circumference of a circle.

## The next lessons are

• Angles of a circle
• Circle theorems
• Prism shape
• Trigonometry

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