Topics
8. Circles
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United States of AmericaVirginia
Grade 6

8.01 Characteristics of circles

Lesson
Practice

Characteristics of circles

A circle is the set of all points that are the same distance from a central point. We call this distance the radius.

A circle with a radius.

\,\\\,\\\,\\\,A line segment joining the central point to some point on the circle is called " radius".

A circle with a diameter.

\,\\\,\\\,\\\,A line segment joining two points on the circle, passing through the central point, is called "diameter".

Exploration

Move the slider to change the radius of the circle. Check the boxes to reveal different characteristics of the circle.

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  1. What do you notice about the relationship between the radius and diameter of the circle?
A circle with a diameter split into 2 radii.

\,\\\,\\\,\\\,The diameter is equal to twice the radius, since any diameter can be split into two radii. d=2r

A circle with a dashed line around its boundary or circumference.

\,\\\,\\\,\\\,The circumference of a circle is the distance around its boundary. We can think of the circumference as the perimeter of the circle.

A circle with a dashed line connecting two points on its circumference. The line does not pass through the center.

\,\\\,\\\,\\\,A chord is a line segment connecting any two points on a circle. A chord may or may not go through the center of a circle. The diameter is the longest chord of a circle.

Examples

Example 1

For this circle:

A circle with a diameter of 10 centimetres.
a

What is the diameter of the circle?

Worked Solution
Create a strategy

Find out how long the line is that goes through the middle of a circle and touches the edge at two points that are opposite each other.

Apply the idea

Look for a straight line that goes from one side of the circle to the other, passing through the middle. This line is called a diameter, and its length is 10\text{ cm}.

\displaystyle \text{Diameter}\displaystyle =\displaystyle 10 \text{ cm}
b

What is the radius of the circle?

Worked Solution
Create a strategy

Remember the radius is half the length of the diameter.

Apply the idea

In part (a), the value of the diameter is provided as 10\text{ cm}.

\displaystyle \text{Radius}\displaystyle =\displaystyle \dfrac{10}{2}Divide 10 by 2
\displaystyle =\displaystyle 5 \text{ cm}Evaluate
Idea summary

A circle has many parts:

A circle with its parts drawn and labeled.

The diameter of a circle is double the radius:

\displaystyle d=2r
\bm{d}
is the diameter
\bm{r}
is the radius

Outcomes

6.MG.1

The student will identify the characteristics of circles and solve problems, including those in context, involving circumference and area.

6.MG.1a

Identify and describe chord, diameter, radius, circumference, and area of a circle.

6.MG.1bi

Investigate and describe the relationship between: i) diameter and radius;

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