Lesson video

In this lesson we're going to learn the parts of a circle.

It's important that we know the parts of a circle.

As these words crop up in a lot of topic areas that involve circles.

So let's start with the circumference.

Circumference is the outside edge of the circle.

Or the perimeter of the circle if you will.

Every single point on the circumference is exactly the same distance from the centre.

Now we have the diameter, a diameter goes from one point on the circumference to another but it must pass through the centre.

A radius goes from the centre to any point on the circumference and therefore the radius is exactly half the diameter.

Or the diameter is double the radius.

Here we have an arc.

An arc is just part of the circumference.

It can be less than half the circumference.

It can be more than half the circumference.

It can be exactly half the circumference.

It doesn't matter its just part of the circumference.

Now here we have a chord.

A chord goes from one point on the circumference to another but unlike the diameter it doesn't pass through the centre.

Here we have a segment.

A segment is an area bounded by and arc and a chord.

Bounded by means surrounded by or has a boundary of the arc and the chord.

So these make up the outside edges of the segment.

Where as a sector is the area bounded by two radii that's what we call the plural of radius and an arc.

Here are some questions for you to try.

Pause the video to complete the task and restart the video when you are finished.

Here are the answers, did you notice in question two that whatever the radius is the diameter will always be twice as long.

And whatever the diameter is the radius will always be half this length.

Here is another question for you to try.

Pause the video to complete the task and then restart the video when you are finished.

Here are the answers.

Sometimes we build up a picture in our minds of what something looks like and because arcs are often drawn which is less then the circumference it can be easy to forget about these that are greater than half the circumference.

Here is a further question for you to try.

Pause the video to complete the task and restart the video when you're finished.

Here are the answers so the similarity of the word sector and segment and the fact that they both describe part of the area of the circle does mean that they can often become confused.

Remember the word sector might crop up in the topic of Pie charts and maybe you could think about when they're used in everyday language such as an orange segment.

Let's look at a question that uses the properties of circles in particular diameters.

So here we have a circle drawn on a coordinate grid it's just a sketch grid and a diameter is drawn from point to now what are the coordinates of the centre? Well the centre of the circle is also the midpoint of the diameter so if we find the midpoint of these two coordinates then we've got the centre of the circle.

So what we do is we take the X coordinates of -2 and 10 and we add them together and divide by 2.

And we do the same with the Y coordinates.

We had to get the 3 and 13 and divide by two.

So here we have 8/2 for our X coordinate and 16/2 for our Y coordinate.

So here we are final answer the centre of the circle is so this question is just another way of asking for a midpoint of two points.

Lets look at a slightly different question.

So this time we know that the centre of the circle is and we know one of the points on the circumference is we have a radius drawn to it.

We're going to extend that radius to form a diameter.

So keeping that straight line if we extend it on the sketch diagram all we need to do is find the missing coordinate.

Now this is the centre and one of the points on the circumference so the best thing to do is to work out how is the X coordinate changed going from the point on the circumference to the centre.

So we've got negative seven to negative one so we've added six so let's add another six and that takes us to positive five.

Let's do the same to the Y coordinate.

Negative three to negative six is subtract three so let's subtract another three and that gives us negative nine.

Now if you want we could work out the midpoint of and but we would find it is of course.

Here's a question for you to try.

Pause the video to complete the task and restart the video when you are finished.

Here are the answers if you weren't sure about your answer to part B then a method for just verifying whether its correct would be to find the midpoint of your answer and and if that came out as then you know that you've got the right answer.

That's all for this lesson thank you for watching.