Let's do this question, the sakalys inscribed in Triangle Park, you are always the center of the circle,
given that angle or D is seventy five degree find angle copy.
All right.
Pause the video, give it a try and then let's do it together.
All right.
Let's do it together.
Over here.
The circle is inscribed in Triangle Park.
You are right there for the circle is the inner circle of Triangle Epicure.
We have learned about the inner circle in triangles.
Right there in the center is the point of intersection of the angle by right.
And using that point, you find the entry it is and you can draw an inner circle for a triangle.
All right.
Over here, this circle is the inner circle of Triangle Peak.
You you're right.
That means that these angles are equal to 90 degrees.
Right.
But these angles are equal to 90 degrees.
Right.
And peak, you you are A and B are tangents to this circle.
All right.
Let me know that over here, so these three are tangent to the circle.
All right.
Therefore, we know that this distance over here, if I say this is a and let this be D, then Kuai
and Kudi will be equal.
Right.
Because these are tandyn from an exterior point to a circle.
Let me call it of X and X.
Similarly, these two will be equal, so that can be Y Y.
Similarly, these two lines are equal.
So let it be Z NZ.
All right.
Now, we know that the band instruments are from an exterior point are equal.
So that's why we have found that these two are equal.
These two are equal and these two are equal.
All right.
Now, you can notice one more thing over here or A or B and or if these are also of equal length.
Right.
Because these are radii of the inner circle to always equal is equal to or F, right.
Now, let's mark this point as Ian if.
OK, so.
Over here, you can see that D or F, that's me or F ah, this shape over here, right?
This is a kite.
Remember we learned about kites and the quadrilaterals, but this shape is a kite that we know that
over here the offer is a kite and in a kite the bigger diagonal is the angle bicycle.
Right.
Therefore angle or the will be equal to angle or if that is this angle over here will be equal to this
angle over here.
And it's given that angle or that's this angle over here.
Is equal to seventy five degrees.
All right, so we have these two seventy five degrees now.
Let's mark these angles, this angle one and two and three and angle for you will see that angle.
One is equal to angle two and angle three is equal to angle four.
Why is that so all here Q, E or B is a kite and you always the bigger diagonal to the bigger diagonal
is the angle bisected in a kite.
So that's the angle.
One is equal to angle to similarly B, E or F is also a kite.
Right.
And in the kite the bigger and bigger diagonal is the angle by sector angle three is equal to angle
four.
Now remember, what was the criteria for it to be a kite?
Two sets of a decent side should be equal.
So in all these three cases that is D or F are due east or D and B, E, or if you can see that they
have two sets of adjacent sites as equal, for example, in the or F are different R and if are equal
and all and F are equal because these two are really.
All right.
Now let's add a piece to angle one plus angle two plus angle three plus angle four.
If you add up all of these right, how much will you get.
That would be 360 minus seventy five plus seventy five because well here we know this angle is seventy
five degrees.
Right.
And we know this angle is seventy five degrees.
But if you add all these angles it makes one complete revolution.
So that's a 360 degree.
Now if you just want one plus two plus three plus four, that's 360 minus seventy five plus seventy
five.
That gives you two hundred and ten degrees.
Right.
All right.
Now what is asking the question you need to find angle cupie.
That's cupie.
That's angle two plus angle three.
That is what you need to find.
And you can see that angle two plus angle three is the same as two hundred and ten by two.
Right.
Because angle one plus two plus three plus four is two hundred and ten.
That's what we got over here and we know one and two are equal and three and four equal.
So I can write this as two times angle two plus two times angle three is equal to two hundred and ten.
Therefore angle two plus angle three will be equal to two hundred and ten by two.
That's equal to one zero five degrees.
And that is the answer to this question.