Let's do this question, B, X, Y, C is a rectangle.
All right, it is A and B, C are tangents.
These three lines of tangent to the circle or is the center of the circle.
All right.
Diagonals B and C X meet at all angles.
B, AC is equal to 40 degree find angle X or Y.
Pause the video, give it a try, and then let's do it together is a very good question.
All right, we are back.
I hope you have given it a try.
Let's do it together.
Let's join all with B, B, F, C and E right over here.
We join with these points and let's join up with X and Y also.
Now, remember, it's given that X, C and B, why meet at all?
Right, this this Beevor is a straight line and C, X is a straight line and they meet at all.
But we know angle X or Y will be equal to angle B or C, right.
Why is that so.
Because these are vertically.
All right, so over here, you can see that video F and F or E, C, these two are kite's, right?
Why is that?
So let's take, for example, Biery off over here or is equal to or F because both are radiuses of the
circle.
Right.
So what is equal with and really is equal to be because B and B if are tangent to the circle from an
exterior point.
But whenever you don't draw tangents to a circle from an exterior point, they will be of equal length.
We learn more about this in this section on circles.
All right.
So we have two sets of equal sides.
Therefore, beauty or F is a guide.
And similarly, F or E, C is also a kind because all F is equal or and F is equal to see.
Why is F.C. C because the attendance from an exterior point to this circle.
All right.
Now, in a case we know, that long diagonal is an angle bisecting.
Right.
The long diagonal is an angle by sector, therefore in beedi, or if this angle and this angle will
be equal.
Similarly, in F or easy angle, FLC and C E will be equal.
Let me market us X and X and Y and Y.
All right.
Now you can see that 80 or E is also a kite.
Why is that?
So you have it equal to A and you have B or is equal to only deal is equal to only because they are
radiuses and it is equal to a because they are tangent from an external point to a circle they'll be
of equal.
Right.
All right.
Now over here.
Let's mark this as 1990, we know they are 90 degree because 80 and E are tangents.
It's given in the question.
Right.
And tendons form a 90 degree angle when you draw a line from the point of intersection of the tangent
to the center of the circle.
All right.
So this angle is 90, this angle is 90.
That's how we define a tangent.
All right.
So angle to the or it will be equal to 360 minus 90.
Minus 40.
Right.
Why is that so?
Because it is a four sided polygon.
The sum of the internal angles of a quadrilateral is equal to 360.
We know this angle is 90, this is 90 and this is 40.
Right.
So therefore, this angle over here, that's the only has to be 360, minus 90, minus 90, minus 40.
That's equal to 140 degrees.
All right.
So angle B or C, which is X plus Y will be equal to half of angle D.O.C. That's 70 degrees.
Right, because body is equal to two X plus two way and B or C is X plus white.
All right, so we know that X or Y is equal to B or C, right?
Therefore X or Y angle, X or Y also is equal to 70 degrees.
And that is your answer.