Let's do this question, Asaka with Dimitar, SPQR.
All right, is inscribed inside a triangle ABC.
So this is the diameter and you have Triangle ABC and this circle is inscribed inside this triangle.
The circle meets the triangle at R.
S and Z always is the center of the circle.
B is the point of intersection of our Q and B as to argue and P Es are meeting at point B the diameter
of the circle is two centimeter.
Find angle S or R.
S or that's what you need to find out.
If Angle Pudi Q that's b b q this angle is given us two times angle as well.
S who are already was the video.
Give it a try and then let's do it together.
All right.
We are back.
I hope you have given it a try.
Let's do it together.
Let's join up with S and ah.
OK now you can see that these two angles that is all s e and angle or are it will be ninety degree angles.
Right.
Why is that.
So it's mentioned that this circle is inscribed inside this triangle right there for a BBC and AC will
be tangent to the circle.
And we know that if you join the centre to the point of intersection of a tangent and a circle, you
get a ninety degree angle.
So over here you have a ninety degree angle and over here you have it.
Ninety degree angle.
Remember this circle over here is the inner circle of this triangle.
Right.
And this is the in the center of this triangle.
Let's proceed.
So.
Anchor desk, you will be equal to 90 degree Y will be equal to 90 degree angle to is the same as angle
B skew.
Right, both of them are the same.
You can see that from the diagram.
But these this angle will be 90 degrees because it's the angle sub-standard by a diameter.
Right.
Let me clean this up a little bit, but these two will be equal and hence angled skew will be equal
to 90 degrees.
All right.
Now, whatever angle petechia in, you see that angle B, B, Q, that is this angle over here is an
external angle to triangle SPQR.
Right to be recut is obtained by extending side.
Yes, that's right.
Angle PDU is an external angle.
The triangle is dequeue.
Therefore Angle PD Q is equal to ninety degree plus angle is Kutty.
Right, because this angle over here that's angle D.
Q is ninety degree angle pd.
Q is angle dsu plus angle secuity.
Because there's an external angle and we know that external angle is equal to some of the interior opposite
angles.
And over here we have seen that Vesku is ninety, so I have Sub-Zero ninety degrees over here, so that
is equal to 90 plus angle s or BITOU.
Why is that so angle s or is this angle over here and angle is too deep.
Is this angle over here.
You can see that angle is skewed.
The or askew arc which is the same angle is the angle.
SUB-STANDARD by arc is to that will be half of the measure of the arc, the measure of the arc Odyssey's
are right.
So that's why we have an angle skewed as half of angle as or so.
That's one of the properties that we have discussed before.
So therefore I can write this also as equal to two times.
So why is that?
So this is because it's given over here.
Angle PD Q is two times angle and so it's mentioned over here.
So now I can solve this.
I saw by two over here and I have two times as well over here now solving this I get three by two angles
or is equal to ninety degree or angle is or is equal to sixty degrees.
And that is the solution to this question.