Lesson video

Hello, I'm Mr. Coward, and welcome to today's lesson on parts of a circle for today's lesson all you'll need is a pen and paper or something to write on and with.

If you can take a moment to clear away any distractions, including turning off any notifications, that would be great.

And if you can, try and find a quiet space to work where you won't be disturbed.

Okay, when you're ready, let's begin.

Okay, so time for the Try this task.

So I would like you to use these words to describe what is the same, and what is different about these shapes.

So, pause the video and have a go, pause in three, two, one.

Okay, welcome back.

Now.

let's start with edges and vertices and I'm going to ignore the circle for now.

This has four edges and four vertices.

This has three edges and three vertices.

This has five edges and five vertices.

It's quite easy to see and count them, and it's very clear what the edges and vertices are on these shapes.

Oof, where on this one? I mean, that's a, that is a very, kind of, I mean, I don't, I don't know if there's a consistent answer for this.

Some people, would say that there's one edge.

Some people would say that there's zero, and some people would say that there's actually infinitely many tiny, tiny, tiny, tiny, little edges.

Who's correct? I'm not actually sure of that.

In vertices, is it zero or is it infinity? And, I think that the point of this is to highlight that, these we have straight lines with distinct corners.

Okay, so we have straight edges with distinct vertices.

Whereas this one, we don't, and it's this one is different.

Lines of symmetry.

Well, how many lines of symmetry does it have? This one oops, sorry, that should've been a flat line and because it's a square it has the diagonals as well, which I haven't drawn them particularly well, but from that vertice to vertice, they should be that diagonal there, is a line of symmetry.

This one, because it is an equilateral triangle, it will have, no it's not right.

To scale, it will have three lines of symmetry.

This one will have one two, goin' for the midpoint, three, four, and five.

And you can tell I've actually destroyed this cause they should all actually go through the same point.

But we should have five lines of symmetry for this one.

Well, this one, well, there's a line of symmetry there and if you move it, slightest bit, this should be going through the centre, pretend that's the centre.

If you change it by the slightest, even a fraction of a degree, it's still a line of symmetry.

So this one has infinitely many lines of symmetry.

What about rotational symmetry? How many times would you rotate this and it looks the same? Well than what, if that position, rotate it 90 degrees, and again, 90 degrees, and again, and 90 degrees again.

So it looks the same in four positions so it has a rotational symmetry of order four.

This one, the equilateral triangle, has a rotational symmetry of order three.

This one has a rotational symmetry of order five.

Whereas this one, again, every tiny little bit that you rotate that, it looks the same.

So it has an infinite rotational symmetry.

So the circle, is quite different from the rest of the shapes.

We call these shapes polygons and these are all regular polygons because each side's the same.

This one is not polygon, this one has a curved edge.

We're going to be looking at circles and focusing on them.

So, decide which of the following shows the radius.

Hmm, well what is the radius? Well, you're going to hopefully be able to find out.

This one, this does show the radius.

This one, does not show the radius.

Does this one? Yes.

Does this one? No.

Does this one? Yes.

Does this one? Does this one? Does this one? Hmmm? What is the radius? Can you work it out? Well, the radius, is the length of the line, segment that goes from the centre of the circle to the edge.

So the radius, is the length of the line, that goes from the centre to the edge of the circle.

So it can't go past the centre, it can't go outside the circle, it must go exactly from the centre to the edge of the circle and it's however long that line is, is the radius.

Now it comes from the Latin word, "Ray" or "Rod".

And, the word ray, you can kind of see it is like a ray of light coming out from the centre or rod, perhaps makes more sense.

And, when you think about it was a rod on a chariot wheel, so these were the rods on the chariot wheel.

So you can kind of see how that's the radius.

Okay, so now we're going to learn another new word.

We're going to learn the word, diameter.

This one? Is this the diameter? Yes.

Is this one? No, what's that? Well, that's a radius here.

Is this one? Yes.

Is this one? No.

This one? Yes.

This one? No.

This one? So what is a diameter? Well a diameter, passes from one edge of the circle, to the other edge, going through the centre.

Okay, so it must go from one edge to the circle, to the other edge, going through the centre.

So, the diameter is the length of a line segment that goes from one edge of the circle, to the other, passing through the centre.

So it must go through the centre and it must go from one edge to the other.

Okay, so here is the radius and here is the diameter.

What is the relationship between the radius and diameter? Can you see it? If the radius was six, what would the diameter be? If the diameter was 15, what would the radius be? So you might want to pause the video now and have a think about that.

Okay, so hopefully, you can see that this, radius is half of, the diameter, or the diameter, is double, the radius.

So the radius, is equal to half of the diameter and, I'm going to use "r" and "d" here just cause I'm being a bit lazy.

So the diameter equals two times the radius, and you don't even actually have to write the times sign, you could write that out like that.

Okay, the diameter, equals or is equal to, two times the radius.

So, if the radius was six, what would the diameter be? Double.

If the diameter was 15, what would the radius be? Half.

So, to get from one to the other we just double, or we just half it.

So, I would like you, just to pause the video and have a go at this quick task, so pause in three, two, one.

Okay, welcome back.

Hopefully, you found that radius here, was four and the diameter was eight.

And I'll remember my units.

Hopefully you got the radius was three, and the diameter was six.

Now what about this one? Well, can you see how that length of 13 is the same as the diameter? So that's 13 and that's 6.

5.

What about that? Well, that's a square, that's five, that's five and that's five.

We've got that the radius is five.

The radius is five and the diameter is 10.

Okay, so really, don't really know if you've got them and if you struggled on those last two, don't worry, they are quite tricky.

Okay, so next bit of language we're going to learn, a sector, okay.

So a sector, is "A region of a circle enclosed by two radii and the circumference." So that means it's in between, two radii, so two.

So the plural of radius, it's radii, so we've got two radii here and it is just, that area here, so that is a sector, okay, circumference, in between two radii.

And you don't have to draw out the rest of the circle, you can just have a sector like that.

You can have a bigger sector.

And quite often people think this one looks like Pac-Man.

This one, this one is not a sector.

Why is that not a sector? Well, because, these two, it needs to have two lines that are radiuses of the circle or radii of the circle.

And that line, is one line.

And even if it was split into two, they wouldn't be radii, or radiuses.

Okay, so an arc, "An arc is a fraction of the circumference of the circle." So that length, that there, is an arc.

That is an arc.

And, that is an arc.

A chord.

"A line joining two points of the circumference of a circle without going through the centre." So it goes through two points, on the circumference, but it does not go through the centre.

So why isn't this one a chord? Because it goes through the centre.

A segment.

"the area contained by an arc and a chord." So this, is a segment.

Because, that is a chord and it's the area contained by a chord, and an arc.

Whereas this, this is not, because, that and that, they aren't chords, they are radii.

So what's this than? Well this, that's a sector.

Okay, and final one, a tangent.

A tangent is "A straight line that touches the circle at a single point but does not pass through it." So it just touches there, but does not go through the circle.

Okay so now it's time for the Independent task.

I would like you to pause the video and complete the task and resume once you finish.

Okay, welcome back, here are my answers, you may need to pause the video to mark your work.

Okay, so now it's time for the Explore task.

We have three identical circles that fit exactly inside a rectangle with 72 centimetres.

How many missing distances can you find? So, pause the video to complete your task, resume once you've finished.

Okay, so I'm going to work through some of the things that I managed to find.

Now you might've found more things or less things than me, and that doesn't matter.

You might've found different things.

You might've found things that I didn't find.

It's just about finding as many things as you can.

So, first thing I'm going to do, is well, I've got three circles and they're identical, so that length, must be a third of that.

So I want to find a third, of 72.

Well, a third of 72 so 72 divided by three.

Well, 60 divided by three is 20, and I've got 12 more.

So 12 divided by three is four.

So I have 24.

So a diameter, of one of the circles, is 24.

Which means that what is the length of the radius? 12, so we've got a radius of 12.

Where's that, goin' that way's 24.

A line goin', that way, goin' up, is also 24.

So I can find that, now I could even find out the area of my rectangle, by doing 72, times 24 to find the area of that.

Well, okay, if that's 24 and the radius is 12, well that's 12 plus 12 plus 24, 48.

So I've got that line.

Hmm, what else could you work out? I don't know, is there other things you could find? May be, and this is the opportunity for you to explore, and you need to find everything that you can.

So, hopefully you enjoyed that lesson, and that is everything for today.

Thank you very much for all your hard work and I look forward to seeing you, next time.

Thank you.