Let's do this question, a circle with diameter as P.
Q is inscribed inside triangle ABC, the circle meets the triangle at R.
S and Z, always the center of the circle.
This is the point of intersection of argu and B.S. that's over here.
The diameter of the circle is two centimeter.
Find a oh e or if angle puti q b the Q is two times angle s or s or.
All right was the video.
Give it a try and then let's do it together.
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We are back.
I hope you have given it a try.
Let's do it together now.
Let me join our OR and OS.
All right, now, these two angles will be 90 degrees because a is a tangent to the circle and AC is
a tangent to the circle, right, because it's mentioned that this circle is inscribed inside the triangle.
So this is actually the inner circle of triangle ABC.
Right.
And we know that this will be 90 degrees.
And over here, it's also mentioned that the circle meets the triangle at artists and the.
All right.
So these two angles will be 90 degrees right now.
Let's join S and Q.
OK, now you can see that angle, the skew, the askew or angle B skew, both are the same.
They are equal to 90 degree right angle.
Popescu is equal to 90 degrees.
Why is that so.
Because it's the angle sub-standard by the diameter Piku.
Right.
So and you can see that angle dsu an angle.
You are one and the same angle.
So let me write it as angle.
DSU angle is equal to 90 degrees.
Right.
And you can see that angle cube.
That's B the Q this angle over here is an external angle to triangle as the dequeue.
Right.
Why is that.
So you extend D to form this angle over here.
Petechial right now.
Can you remember an important property with respect to triangles and external angles.
Yes, the external angle will be equal to the sum of the internal opposite angles.
Right.
Therefore I can say that Angle Q is equal to 90 degree plus angle is the right y ninety over here because
Bascule is equal to 90 or Priscu is equal to angle DSU plus angle is skewed and instead of angled skua.
Right.
Ninety over here now instead of angle escudo I can write half of angle s or are right.
So that's equal to 90 plus half of angle S or no.
Why is that so.
Well over here you can see s Q D is the same as ESC.
You are right, both of them are this angle and that angle is the angle made by arc are s rated.
It's by Arc Argyris and we know that the angle subtenant by the arc will be half the measure of the
arc.
What is the measure of arc that would be S or are right.
We just need to join these two points to the center.
So Angle s will are is the measure of the arc and s Q D This is the angle subtenant by the arc, so
this will be half the measure of the arc to a right angle.
So are two.
Now this over here is equal to two times angle or because it's given right angle.
Petechia is two times angle s or so that's given.
So therefore I can solve for angle Isaw.
That's three by two angle Asla is equal to ninety degree or angle s or is equal to sixty degrees.
All right, now let's proceed.
You can see that a R or S is forming a kite.
Right.
A R or this is a kite.
Why is that so.
R is equal to S because we are an s are the engines from an external point to a circle and or are is
equal to or less because both of them are radii of this circle right now.
We know that in a kite it has two sets of adjacent sites equal.
Therefore a R.
S is a kite.
Now let me join E and all over here you can see that this is the bigger diagonal.
And in a kite, the bigger diagonal is the angle sector right now.
Over here we got that S or R is equal to sixty degrees.
Therefore this angle over here, D or R will be sixty by two.
That's equal to thirty degrees.
Right.
All right.
Now let's apply our knowledge in trigonometry cos thirty over here will be equal to or divided by equal
right.
So cost thirty is equal to or by equal.
Always the hypotenuse.
Right.
And that's equal to one divided by you.
Right.
Because it's mentioned that the diameter is two centimetre.
Right.
Therefore the radius are all that would be one.
Right.
Therefore the radius is one.
So you get one by L is equal to custody.
Now we know the value of course that is equal to rule three by two.
So that gives us room three by two is equal to one by equal or you get the value of us two by three.
And that is the answer to this question.