Students, welcome to the section where we deal with circles.
Let's get started with the basics.
Let's take an example of a circle.
So this type of a shape is called a circle.
You can see that it is a simple closed curve, right?
Remember, simple means.
It does not cross itself and closed means it's not open.
All right.
Now, in this circle, you can see that every point on the circle is at an equal distance from the center.
So that's the defining characteristic of a circle over here.
This is the center of the circle.
And you can see that every point on the circle, that is all these points are at the same distance from
the center.
So let's take a few points on this circle.
So we have point A, B, B and E taken on the circle.
So what have we learned over here?
We have seen that if we join these points to the center, then these lengths are equal.
That is C is equal to see.
B is equal to the galaxy.
All right.
Now let's take one of them.
So let's take for example, see, now this length is called the radius of the circle.
Now, over here, the radius is the singular.
Now, if you take multiple radius, as you call it, really, I'm all right.
Now, let's take the radius as are now over here.
If you observe E, this is a line segment that passes through the center.
So this type of a nine segment is called the diameter of the Circle.
And that's equal to two times are right because it C is equal to are and C is also equal to up to 80
is equal to two times are now.
Earlier we had learned that in the case of a line, you just need two points, right, to define a line
because through two given points, only one line can be drawn.
Right now if you take just two points, you will see that you can draw multiple circles through two
given points to define a unique circle, you will need three points so only one circle can be drawn
through three given points already having established the basics of a circle.
Let's move on and learn some of the important terms in the case of circles.
All right.
We start with the card.
Now, this is an example of a card.
This is called P.
Q that is a card connects two points on the circle.
Now, if these were extended and if it's like a line segment like this, then you can call this second.
All right, now let's press on over here, let me take any two points on this circle at this point and
point B now this measure over here is what you call an arc.
This is the arc.
That is it is a portion of the circle.
It's a portion of the circle.
All right.
Now, over here, you can see that this is the minor arc.
And if you draw it like this, this would have been called the major arc, Abe.
All right.
So we have a minor arc and we have a major arc.
So the minor one is a smaller one and the major one is the bigger one, this part over here.
All right, now you the northern arc, either by writing arc or you have this type of a shape over here.
All right.
Now, let's move on to a sector.
What is a sector of a circle?
It's an area enclosed by an arc and a pair of radiate.
But what does that mean?
Let's take an example.
It's enclosed by a pair of really and it's enclosed by an arc.
We know what radiuses and we know what an arc is.
So let's combine these two together.
So this area, for example, is called a sector.
All right.
Now let's move on to segment.
What is a segment?
A segment is an area enclosed by a code and anarch.
So we know what the code is.
We've learned that over here.
Right.
And we know what an ark is.
We have seen this is, for example, an ark.
But let's combine these two together.
So over here you have a segment.
So this is a segment.
Now, remember, as in the case of an ark, you have a minor ark and major arc over here.
Also, you have a minor sector and you have a major sector.
This is the minor sector.
OK, and over here also you have a minor segment.
This is the minor segment.
Let me write that over here and this pot over here, the outside of the circle, that would be the major
segment.
All right, now let's move on.
What is the circumference of a circle?
What does that mean?
It's equivalent to the perimeter of polygons, right?
For example, in the case of a rectangle or square.
We have seen that if you add the length of the borders, you get perimeter.
Right.
The same thing in the case of a circle is called circumference.
So it's the distance around a circle.
For example, over here I have another circle.
If I move around it one time, this length over here is called the circumference of the circle.
Now, over here, this is the center of the circle.
Let me draw a line through the center.
Now, you can see that this line over here is a diameter.
We have already seen that.
And you can observe that the diameter divides a circle into two equal parts.
So this part over here and this part of here is of the same area.
So the diameter divides a circle into two equal parts.
Now, if you take one such part, that is what we call a semicircle.
All right.
Let's quickly revise what we've learned in terms of terms in this section.
We have learned that a cord connects two points on the circle.
So, for example, P.
Q is a cord.
We have seen that an arc is a part of a circle and we have seen that a sector is enclosed by two really,
and an arc and a segment is enclosed by an arc and cord.
We have seen the circumference is the distance around the circle and this is what we call a semicircle.
It's formed by diameter.
All right.
Now let's learn a few more important terms in the case of a circle.
Now, over here, I have a circle and I have arc over here.
Now we start with measure of an arc.
What do we call the measure of this arc?
Let me join A and B to the center of this circle.
All right.
Now, this angle over here is what we call the measure of the minor arc.
Remember, this is the minor arc, right?
This is my in Iraq, Abe.
And therefore the angle substandard by the minor arc at the center.
That is this angle over here is what is called the measure of the minor.
Similarly, this spot over here is the major arc, Abe.
Right.
Let me draw that.
So this part over here is the major arc.
Abe, right now, if you see that this is the angle suspended by the major at the center right.
So that is called the measure of the major arc, Abe.
All right.
Now, an interesting thing to note over here is you will see that if you add these two points, these
two angles together, you get one complete revolution around a point.
Right.
And therefore, this measure plus this measure that is a measure of the major Ebbie, plus the measure
of the minor Abe will give you 360 degrees.
All right.
Let's continue.
We have seen what we mean with the measure of an arc right now.
Let's see what we mean with an inscribed angle in another or the angle supplemented by an arc.
Over here you have arc, Abe.
Now, let's take a point C over here and you see that angle ACB That's this angle over here is the angle
suspended by our Abe at a point, see.
All right.
So this is something that we will see in future lessons also because there is an interesting property
associated with this.
But let me keep that for a future video.
All right.
Now, let's go ahead with understanding various terms of a circle at point C.
Let me draw a tangent.
So that's a tangent at point C, right.
Lynelle is a tangent for L is a tangent to the circle.
Let's see now.
What does that mean?
What is a tangent?
A tangent is a line that touches the circle at only one point.
It can be only at one point.
Right?
It has to be exactly at one point.
Now, if it touches a two points, it would look like this right across this line.
If this line touches the circle at two points over here and here, then this line is called the second.
So we have seen what we mean with a tangent and we have seen what we mean with the second.
All right.
Now let's learn one more interesting thing about tangents over here and at this point all.
And let me correct that two point to point.
Or is the center of this circle and buoyancy is the point at which tangent l touches this circle.
Now, over here you will see that this angle over here, that is the angle formed between the tangent
and the radiate right through the point of intersection of the tangent at the circle.
That angle is equal to 90 degree, but and in that radius form a 90 degree angle.
So that's also a very important property.
And we will see more about that in future.
Reduce.