Students in this video, let's start discussing some of the interesting properties about a circle which
we will be using in questions.
All right.
Well, here I have a code of this circle and say this is the center of this circle.
All right.
Now, let me name the code as a B..
OK, now let me draw or be over here.
Now, the property says that if OPIS is perpendicular to Ebbie, right.
That means if these two angles are 90 degrees, right.
Then A B will be equal to be that is this distance will be equal to this distance over here.
Now, can you tell me why that is?
So let's quickly think about it.
It's using congruency of triangles.
It's given that opis perpendicular to a right.
But we know that this angle is equal 90 degrees and this angle is equal to 90 degrees.
Now, if you join or and you get over here and over here, if you join, when you get orbit now, all
will be equal to will be because these two are radiuses of the circle right now in Triangle or EPEAT.
And Triangle or BP, you will see that oil is equal to Olby and OPIS is a common sight and this angle
is equal to 90 degrees and this angle is equal to 90 degrees.
But you can see that these two triangles are congruent.
Asper are as congruency, right?
If these two triangles are congruent, then AP will be equal to BP because these are corresponding sides
of two congruent triangles.
All right.
So let me summarize.
If you have a code and from the center, if you drop a perpendicular to the code, then that perpendicular
line is the bisected of the code that is EBP will be equal to.
Now, the converse of this is also true.
That is, if a particular Beeby then or B will be perpendicular to Ebby.
Let me quickly show you why that is so.
So over here we are starting with a particular beebee.
Now again, we have these two triangles over here.
Now, in this triangle, it's given that it is equal to PB.
So this is equal to this.
And we know always equal will be because these are really and OPIS is a common sight.
So Asper assesses concurrency criteria in this case.
We know that triangle or a B is congruently triangle or B B, right.
Why?
It's because of Essence's rule.
We have seen that over here.
Therefore, you know that this angle is equal to this angle and these two former linear pair also that
is this plus this is equal to 180 degree ends.
We can conclude that OPIS perpendicular to EBR or this angle over here, that's angle B and angle OPV
has to be equal to 90 degrees.
All right, let's move on.
So we have learned two interesting things over here.
We have seen that if you have a code and if a perpendicular is dropped to the code, then it will be
equal to Beebe.
We have also seen that if a line is drawn such that a piece equal to be, then OPIS will be perpendicular.
All right, let's continue to over here.
I have taken one more call, let me name it, as ex-wife.
Now the next property says that say you have or On2 ex-wife.
Now, if it is given that OPIS is perpendicular to Ebbe and or are is perpendicular to exwife.
Right.
If this is true, then if Ekso AB is equal to ex-wife, then it will be will be equal to or if AB is
equal to x y then OPIS will be equal to or and the converse is also true.
That is if OPIS is equal to or then AB is equal to x ray.
Let's try to understand that.
What does it mean if you have two courts such that the perpendicular distance from the center to the
courts are equal?
Right.
That's this case over here.
Then the two courts will be of equal length.
Similarly, if you have two courts of equal length, then the distance of the center to those courts
also will be equal.
Now, let's try to understand why this is so.
Now, let's start with assuming that it's given or B and or perpendicular to Abian X Y.
Right.
So based on what we have learned over here, we know that X R will be equal to our way and AP will be
equal to Beebee because these are perpendicular.
All right.
Now, if say it's given that a B is equal to x ray, let's start with this one over here.
This is let me call the three and let this be four.
All right.
Let's start with this third condition.
So it's given that AB is equal to X Y.
All right.
So then we know that B B will be equal to Ottoway, right.
Because this baby is equal to half of AB.
Ottawa is equal to half of X. So if it is equal to sway, Bebe will be equal to our weight.
All right.
Now let's construct all the way over here and let's construct or be over here.
So I have to right angles triangles whose hypotenuse are equal, right.
Because these two are really high and we have a right angle.
And it is given that B is equal to our weight because every X, Y, therefore Asper artist congruency,
these two triangles will be congruent and hence or will be equal to OPIS.
So that's the proof for the third statement.
But you don't need to know the proof, but it helps to retain and solidify your understanding.
At least you should be able to reason it out to yourself.
All right.
What's the next statement?
That statement for over here, if Opie is equal to or said that is the given statement, again, we
can strike these two triangles right now.
If this is given, then we know this side is equal to this side again or will be equal to or B, because
they are really right.
And we know that this angle over here is equal to this angle over here.
Therefore, as per artist congruency criteria, these two triangles are congruent and hence our Y will
be equal to Beeby and because otherwise.
So let me try that over here.
If you get our way is equal to PBH, then two times our weight will be equal to two times Beeby and
two times our way will be equal to X Y two times B will be equal.
Right.
So that's what we have here.
Let me quickly summarize.
We have learned so far these four properties, right, let's make this clean, that we can quickly revise
what we have learned.
All right, so we have learned these four things, but we started with one call.
If you drop a perpendicular to the code, it will bisect the code.
That is a particular Peevey.
The second statement is if you have a line through the center to a code such that it bisects the code,
then that line is perpendicular to the code.
All right.
The third statement that we learned is if you have two codes, you have an x ray.
And if these two are of equal length, then the perpendicular distance of these two codes from the center
will be equal.
That is, if it is equal to x ray or B will be equal to or.
And the fourth statement is that if you have two codes and it's given that the perpendicular distance
from the center to these two codes are equal, then the two codes will be of equal length.