High students in this video, let's continue learning about properties of Sakalys, all right, over
here, I have a circle with Center all, and you can see that a B is an arc.
And this arc is suspending an angle at point B, but that's angle APB.
All right.
Now, an interesting property of Sakalys is that the SUB-STANDARD angle is half the measure of the arc.
Now, what is the measure of ARCHABBEY?
That's the angle.
It will be right.
We have seen before that the measure of an arc is the angle that it's substance at the center of the
circle.
So the measure of Arc AB is angle will be.
And as per this property angle, EPB is equal to half of angle.
It will be.
Now let's try to understand why this is so.
Let me join P to all and extended two point or.
Why do this construction over here that at this point over here?
All right, now, what can you tell me about anger or be this anger over here?
You can see that angle or B is equal to Angle or B, B plus angle or B, B, right.
That's this angle.
Plus this angle.
Why is that so?
Because Angle or B is an exterior angle.
Or Triangle or Bebe.
Right, and we have learned that in triangles, the exterior angle is equal to the sum of the interior,
opposite angles to Orombi is an exterior angle and angle.
OPV and Angle or BP are the interior opposite angles.
Right.
But that's why this is true.
Now, over here you can see that OPIS is equal to Olby.
These two are equal because these two are really irate or Pissarides and Albie's radius.
Therefore OPIS equal to or B and hence Triangle or B is an isosceles triangle.
Therefore, we know that these two angles, that is the angles opposite equal sides are equal in an
isosceles triangle.
So these two will be equal, right.
So let me call it as two times angle or B.
So we have seen that R or B is equal to two times or B, B, similarly, you can see that R or A.
Let me write that over here, or it will be equal to two times and will all be.
With the same logic now, if you add up these two together, if you add up these two together, that
should be equal to adding up these two together.
So if you add up R or B Ainaro, you will get A, B or C, that's this angle over here.
Over here.
By adding it up, you get angle B or it's the same as angle AOB.
And when you add up these two together, right, you get two times angle A, B, B, right.
This plus this gives EPB and over here you have two, over here you have a two that's two times EPB.
So therefore you can see that angle.
It will be divided by two gives angle EPB.
That's what we got over here.
So let's quickly revise the property in a circle.
If you have an arc and the arc is attending an angle over here, therefore this angle that is angle
APB will be half the measure of the arc.
That is half of angle.
It will be all right.
Now, let me make some space over here.
Now, over here, we have taken our job as the main Iraq right now, what would have been the case if
Archabbey was the major Iraq?
Let me draw that over here.
So I have a circle, right?
I have Alawa here and I have B over here.
Now we are taking the meds, Iraq.
So that's this sakova here.
Right.
Let this be the center to the measure of the major arc, is this angle right?
OK, let me call this as to top then, if you take an angle over here, let me make this point a point
B that I join it with, and B, to this angle over here will be half of this.
That's theater.
So you need to take it in the correct order.
If you're taking the arc as the major arc, then you need to take an angle on this side of the major
arc.
Right.
If you're taking as a minor arc, then you need to take an angle on this side.
That's the other side of the arc.
Right.
In that case, if this is the order, then this will be to data.
In this case, if this measure is detailed, then this angle over here will be tighter.
Now, let me tell you one more interesting thing.
If you take this point, Peter's over here and join and Peter's right.
Let me make it a straight line.
All right, now over here, you can see that A, B, B and B, B Rush are all four points on a circle,
right?
Later, we will learn that A, B, B, B dash is actually a cyclic quadrilateral.
We will learn about that and in a cyclical little the some of the opposite angles is equal to 180 degrees.
So this angle teeter over here and this angle will be adding up to 180 degrees.
So if this is the order, then this angle over here will be 180 minus detail.
And what would be the measure over here?
We have learned that this will if this is done, this has to be to deter.
So this measure over here has to be two times 180 minus detA.
Right.
That's 360 minus two data.
And that is also valid with what we have learned.
Right.
If this is Dieter, we have learned that this is true, Dieter, and we know that this is one complete
revolution around a point that's equal to 360 degree.
So if this is true, Dieter, then this measure over here will be 360 minus two.
Dieter And that is what we have got over here.
All right.
Let me quickly summarize the points that we have learned so far.
We have seen that you take an hour and you make a point P over here and you make an angle APB.
Then if this is true, this will be equal to Dieter.
That's our first learning.
The second learning is that we should take the right arc.
So in this case, we are taking Archabbey as the minor arc and hence we had to take a point over here
so that this one is the ratio is maintained right now.
If you are taking the major arc, then you need to take a point over here.
And if you join it together, it will still be a one to two ratio.
That is, if this angle is titta, this measure of the major arc will be to titta.
That's our second learning.
Right.
And we have also seen that if I join A, B, B and B, that it's forming a cyclic quadrilateral.
We will learn more about cyclic Waldron's later.
But in this case, if this is Dieter, then this will be 180 minus Dieter because the angles which are
opposite to each other in a cyclic quadrilateral are supplementary.
And we have seen that this holds over here you get three 60 minus two Titta.
And that is also true in the other way.
If we take this as two to then because this forms one complete revolution.
Therefore also this angle over here has to be 360 minus two to.