Circles

Concept sheet | Mathematics
Circles (Grades 5 and 6)

Circles

Moments in the video :

  • 00:00-Introduction
  • 00:27-The centre
  • 00:40-The circumference
  • 00:58-The radius
  • 01:24-The diameter
  • 02:16-The central angle
  • 02:42-Conclusion

What is a circle?

Definition

A circle is a plane figure formed by a curved and closed line. All points on the curved line are located at an equal distance from the centre of the circle (O).

Example:

The yellow and pink dots are at an equal distance from the centre of the circle.

Circle
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The different parts of a circle can be described using specific vocabulary.

Example

Here is a circle and its different parts.

The Parts of a Circle
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What is the circumference of a circle?

Definition

The circumference is the measurement of the line that forms the circle’s contour.

Example:

The Circumference of a Circle
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What is the radius of a circle?

Definition

The radius of a circle is a straight line (segment) connecting the centre of the circle (O) to any point on the circle’s contour.

Example:

The Radius of a Circle
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Important!

The radius can be measured at any point on the circle.

Example:

Different Radii of a Circle

The measurement of the radius is always half the diameter.

Example

This circle has a diameter of |10| centimetres (cm). What is the measurement of the radius?

The Diameter of a Circle
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See solution

What is the diameter of a circle?

Definition

The diameter of a circle is a straight line (segment) connecting two opposite points of the circle and passing through the centre (O).

Example:

The Diameter of a Circle
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Important!

The diameter can be measured at any point on the circle.

Example:

Different Diameters of a Circle

The measurement of the diameter is always twice the radius.

Example

This circle has a radius of |6| centimetres (cm). What is the measurement of the diameter?

The Radius of a Circle
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See solution

What is the central angle of a circle?

Definition

The central angle of a circle is an angle (|\angle|) formed by 2 radii and the vertex is located at the centre of the circle (O).

Example:

The Central Angle of a Circle
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The central angle in the example is written |\angle|AOB.

The measurement of the central angle is always between |0^\circ| and |360^\circ.|

To learn how to measure an angle using a protractor, see the concept sheet Measuring Angles with a Protractor.