Let's do this question.
This is a very important question, and these type of questions are very frequent.
Let's do this or here you have a circle, right?
a.D.A and BCR tangent to the circle and angle.
ABC is equal to Angle HCB.
That's equal to seventy five degrees.
Now we need to find angle C or B, all right.
Because the video give it a try and then let's do it together.
All right.
Let's do it together.
We know that these two angles are equal right angle HCB.
Is equal angle, ABC is equal to seventy five degrees with these two angles.
Seventy five degrees therefore I can find angle eight.
That would be 180 minus seventy five plus seventy five.
Right.
So 180, minus 150 gives you thirty degrees to angle.
It is equal to thirty degrees.
All right, let's proceed.
Let's join all with A, B, F and E.
All right, now we know that these three lines are tangent to the circle, right to these angles have
to be 90 degrees.
All right.
Now you will see that the FBI, that's B or FBI.
This is a kind.
Why is that so, or is it because both of them are radiuses of the circle and Beedi is equal to BSF
because beauty and BFX are tangents from an exterior point to a circle.
Now, you will learn more about this in this section on Sakalys.
Whenever you draw tangents to a circle from an exterior point, they will be of equal length.
That is beedi is equal to be if the beauty is equal to the left and Audy is equal to.
Or if you have two pairs of adjacent sites that are equal and the FBI is a kind.
All right, let's proceed.
Now we know that the longer diagonal is an angle bisecting, so angle one is equal to angle.
Similarly, you will see in F all e c this is also a because of is equal weight and F.C. is equal to
see.
Why is F.C. equal to C because they are engines from an exterior point to a circle.
And whenever you have tendons from an extra point to a circle they'll be equal.
That is Sieff is equal to see.
So you have two sets of equal sides.
And if E C is a kite and in a kite, the longer angled bisects the the the longer diagonal bisects the
angle.
Therefore angled three is equal to angle four.
Right.
All right.
Let me know that down over here now, angrily and angrily, both are 90 degree angles.
Right?
Why is that so?
Because it's mentioned that 80 and 80 are tangents to this circle.
Now, when you have a tangent and the tangent intersects a circle at one point, if you join that point
to the center of the circle, the angles will form will be 90 degrees.
Now, you will learn more about this in this section on circles.
All right.
Now, Angley and Angley are both ninety degree angles, right?
Therefore, you can find that angle the.
All right.
Make some space over here and will be or eat this angle over here will be 360 minus 90, plus 90, plus
30.
Why is that so?
Because A, B or C is a quadrilateral, right, and we know that the sum of the angles of a quadrilateral
is equal to 360 degree.
And we know that this angle is 90, this angle is 90, and this angle is 30.
Right.
So the only has to be 360, minus 90, plus 90, plus 30.
And just as a side note, even 80 or E is also a kite because all is equal to oil and it will be equal
to eight.
All right.
Let's proceed to let's find Angle or that would be one 50 degrees from this equation on solving.
We get angle is equal to 150 degrees.
Now, that is equal to from the figure two times angle two plus two times angle three.
Right.
Because angle one and two are equal and three and four are equal.
So this is two times angle two plus two times angle three, therefore angle C or B, which is what we
need to find, which is equal to angle two plus angle three will be equal to half of one fifty.
Right.
That's one fifty by two which is equal to seventy five degrees.
And that is your answer.