Let's do this question always the center of the circle about the art parallel and EFG and BCR parallel.
So let me mark that ebb's parallel to be an EFG is parallel to VXI, and it's given that the radius
of the circle is two centimeter, but it's more that it's already and Augier, the radius of the circle,
they're equal to two centimeters given an angle, ABCDs equal to 90 degrees.
So this angle over here is equal to 90 degrees.
And it's given that the area of triangle ABC is equal to sixty four centimeter square.
Now the question is find 80 d.g and DC already pause the video, give it a try and then let's do it
together.
All right.
We're back.
I hope you've given it a try.
This is a very good question.
Let's do it together now.
Well, here you can see that triangle or d.g is similar to Triangle B AC.
Can you tell me why that is?
So it's the A rule right now in these two triangles, you can see that angle B is equal to angle.
All right.
That's this angle and this angle.
These two angles are 90 degree angles.
Right.
And you will see that angle is equal to angle C and angle is equal to angle the right.
Let's quickly see why this is.
So why is Angle B equal to Anglo?
You can see that angle B is over here and we have a B parallel to the right.
And in that case we see acts as a transversal and hence this angle over here and this angle over here
will be equal because they are corresponding angles.
Now we have FFG parallel to B.C. and in this case, let's take the east as the transposon.
Therefore, this angle over here and this angle over here will be equal because they are corresponding
angles.
And this angle over here, which is angle B and angle all will be equal and both are equal to 90 degrees.
All right.
So we have seen this criteria now in a similar manner.
You can see that angle is equal to Anglesey.
Why is that?
So if parallel to B.C. and let DC be the transversal so you can see that these two angles are corresponding
angles and angles is equal to angle C.
And similarly, you can see that angle eight is equal to angle the big these two lines, which are parallel
and big easy as the transposon again angle entangled are corresponding angles and they're equal to triangles
of these two triangles that is already and B are equal right now.
Therefore these two triangles are similar.
You could have just checked two angles also because we know if two and those are equal, the third angle
also will be equal now because these two triangles are similar.
We can say that a B is equal to B C, right.
Why is that so in this triangle or is equal to Oji.
Right.
Because both are radiuses and the radius is two centimetre, the oldest two centimetre and Orji also
will be two centimeter.
Therefore, AB and BC also have to be equal.
Right.
Why is that so.
Because we have established that these triangles are similar and we know that ratio of corresponding
sides in the case of similar triangles has to be equal.
What does that mean a.
B.
Divided by all the.
Will be equal to B.C., divided by.
Right, but this ratio has to be equal, but I can take this over here to so from here, let me take
Oji over here and bit down.
So that's equivalent to writing.
Orji, divided by Audy is equal to B.C., divided by Ebbitt and Augean already are two.
So that's two by two, which is equal to one.
Right.
So you can see that B C baby has to be one.
That means a B is equal to B C, so A.B.C. have to be equal.
So we have established this over here.
All right, let me make some space over here.
Right.
We know that the area of Triangle ABC is given a sixty four centimeter square and the area of a triangle
is equal to off base into height right over here because you have a right angle.
Abbey itself is the height.
Therefore, the area is equal to half Ebbe into B.C. and that is equal to sixty four.
Right.
And about equal to B.C..
So you can say that half X.
Into X is equal to sixty four, that is X Square is equal to to sixty four, therefore X will be a square
root of two in the sixty four which is equal to eight root to right.
Therefore we have found that a B is equal to B, C is equal to a two centimeter.
All right, let's move on.
If we know A, B and C and we know this angle is a 90 degree angle as per Pythagoras's theorem, we
can find out what is the value of AC.
AC squared would be A, B squared plus B, C squared right to AC square again.
Right over here is equal to a root to square.
Plus, a draw to square, right?
So how much is that a to the whole square.
Sixty four to.
And I have two of these, so AC Square is sixty four in the two in the two, therefore AC is equal to
square root of two in the two in two sixty four.
And that is equal to sixteen centimeter.
All right.
So we have found that a B is equal to B.C. is equal to eight root two and we have found that AC is equal
to 16 centimeter.
All right, let's move on.
Now we know that all is equal to or equal to two centimeters, right?
So what would it be?
D.G B.G. will be root of two squared plus two square, which is equal to two to as per Pythagoras's
theorem.
All right.
And let me make some space over here.
I'm just cleaning it up a little bit.
All right.
Now we know that Triangle D.C. is similar to Triangle ABC, right?
Why is that?
So Triangle D.C. will be similar to Triangle ABC because of the same reason, right.
What are the angles that are equal?
This angle is equal to this angle.
Right.
And you can see that this angle is a common angle for ABC and ABC.
So you have two sets of corresponding angles equal.
So as a rule, these two triangles also are similar.
And we know that in the case of similar triangles, the ratio of corresponding sides will be equal.
So I can say that D.C., divided by D.C. will be equal to AC, divided by Ebbie, right.
D.C., divided by D.C. will be equal to AC by a.
So it's the same thing as writing DC by AC is equal to D.C. by a bit.
So I've just taken AC over here and this equation over here can also be written like this.
So DC by D.C. is equal to AC by AB.
Now let's move on.
Let's substitute values that we know into this equation.
We know that X equal to 16 centimeter, we know is equal to a two and D is equal to four centimeters.
So that gives us Nisse divided by four is equal to 16, divided by eight through two or B, C is equal
to or two centimeter.
All right.
So what are the things that are asked to find out?
We need to find out 80 and see now what is eighty eight is equal to 16 minus or root two.
Right.
So we know that X equal to 16.
Right.
So for two is D.C. though if you subtract D.C. from AC, you're left with 80.
So that's sixteen minus four or two.
Now the next one is d.g.
We have already found out d.g.
That's Tooru two over here.
Right.
And the last one is D.C. That's what we need to find out.
Let's write D.C. next.
D.C. will be Boru to minus two.
Right.
We know that D.C. over here is four, too.
And we know D to row to D.C. minus d.g will give us D.C. That's four to minus two, which gives us to
rule two.
And these are our three answers.
We have 80, which is equal to 16, minus four.
Two we have D.G, which is Tooru two.
And we have D.C., which is to route to.