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Let's do this question always the center of the circle about the art parallel and EFG and BCR parallel.

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So let me mark that ebb's parallel to be an EFG is parallel to VXI, and it's given that the radius

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of the circle is two centimeter, but it's more that it's already and Augier, the radius of the circle,

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they're equal to two centimeters given an angle, ABCDs equal to 90 degrees.

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So this angle over here is equal to 90 degrees.

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And it's given that the area of triangle ABC is equal to sixty four centimeter square.

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Now the question is find 80 d.g and DC already pause the video, give it a try and then let's do it

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together.

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All right.

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We're back.

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I hope you've given it a try.

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This is a very good question.

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Let's do it together now.

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Well, here you can see that triangle or d.g is similar to Triangle B AC.

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Can you tell me why that is?

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So it's the A rule right now in these two triangles, you can see that angle B is equal to angle.

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All right.

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That's this angle and this angle.

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These two angles are 90 degree angles.

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Right.

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And you will see that angle is equal to angle C and angle is equal to angle the right.

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Let's quickly see why this is.

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So why is Angle B equal to Anglo?

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You can see that angle B is over here and we have a B parallel to the right.

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And in that case we see acts as a transversal and hence this angle over here and this angle over here

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will be equal because they are corresponding angles.

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Now we have FFG parallel to B.C. and in this case, let's take the east as the transposon.

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Therefore, this angle over here and this angle over here will be equal because they are corresponding

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angles.

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And this angle over here, which is angle B and angle all will be equal and both are equal to 90 degrees.

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All right.

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So we have seen this criteria now in a similar manner.

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You can see that angle is equal to Anglesey.

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Why is that?

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So if parallel to B.C. and let DC be the transversal so you can see that these two angles are corresponding

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angles and angles is equal to angle C.

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And similarly, you can see that angle eight is equal to angle the big these two lines, which are parallel

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and big easy as the transposon again angle entangled are corresponding angles and they're equal to triangles

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of these two triangles that is already and B are equal right now.

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Therefore these two triangles are similar.

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You could have just checked two angles also because we know if two and those are equal, the third angle

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also will be equal now because these two triangles are similar.

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We can say that a B is equal to B C, right.

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Why is that so in this triangle or is equal to Oji.

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Right.

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Because both are radiuses and the radius is two centimetre, the oldest two centimetre and Orji also

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will be two centimeter.

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Therefore, AB and BC also have to be equal.

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Right.

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Why is that so.

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Because we have established that these triangles are similar and we know that ratio of corresponding

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sides in the case of similar triangles has to be equal.

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What does that mean a.

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B.

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Divided by all the.

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Will be equal to B.C., divided by.

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Right, but this ratio has to be equal, but I can take this over here to so from here, let me take

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Oji over here and bit down.

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So that's equivalent to writing.

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Orji, divided by Audy is equal to B.C., divided by Ebbitt and Augean already are two.

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So that's two by two, which is equal to one.

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Right.

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So you can see that B C baby has to be one.

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That means a B is equal to B C, so A.B.C. have to be equal.

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So we have established this over here.

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All right, let me make some space over here.

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Right.

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We know that the area of Triangle ABC is given a sixty four centimeter square and the area of a triangle

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is equal to off base into height right over here because you have a right angle.

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Abbey itself is the height.

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Therefore, the area is equal to half Ebbe into B.C. and that is equal to sixty four.

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Right.

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And about equal to B.C..

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So you can say that half X.

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Into X is equal to sixty four, that is X Square is equal to to sixty four, therefore X will be a square

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root of two in the sixty four which is equal to eight root to right.

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Therefore we have found that a B is equal to B, C is equal to a two centimeter.

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All right, let's move on.

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If we know A, B and C and we know this angle is a 90 degree angle as per Pythagoras's theorem, we

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can find out what is the value of AC.

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AC squared would be A, B squared plus B, C squared right to AC square again.

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Right over here is equal to a root to square.

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Plus, a draw to square, right?

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So how much is that a to the whole square.

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Sixty four to.

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And I have two of these, so AC Square is sixty four in the two in the two, therefore AC is equal to

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square root of two in the two in two sixty four.

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And that is equal to sixteen centimeter.

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All right.

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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

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to 16 centimeter.

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All right, let's move on.

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Now we know that all is equal to or equal to two centimeters, right?

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So what would it be?

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D.G B.G. will be root of two squared plus two square, which is equal to two to as per Pythagoras's

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theorem.

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All right.

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And let me make some space over here.

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I'm just cleaning it up a little bit.

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All right.

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Now we know that Triangle D.C. is similar to Triangle ABC, right?

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Why is that?

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So Triangle D.C. will be similar to Triangle ABC because of the same reason, right.

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What are the angles that are equal?

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This angle is equal to this angle.

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Right.

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And you can see that this angle is a common angle for ABC and ABC.

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So you have two sets of corresponding angles equal.

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So as a rule, these two triangles also are similar.

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And we know that in the case of similar triangles, the ratio of corresponding sides will be equal.

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So I can say that D.C., divided by D.C. will be equal to AC, divided by Ebbie, right.

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D.C., divided by D.C. will be equal to AC by a.

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So it's the same thing as writing DC by AC is equal to D.C. by a bit.

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So I've just taken AC over here and this equation over here can also be written like this.

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So DC by D.C. is equal to AC by AB.

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Now let's move on.

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Let's substitute values that we know into this equation.

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We know that X equal to 16 centimeter, we know is equal to a two and D is equal to four centimeters.

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So that gives us Nisse divided by four is equal to 16, divided by eight through two or B, C is equal

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to or two centimeter.

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All right.

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So what are the things that are asked to find out?

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We need to find out 80 and see now what is eighty eight is equal to 16 minus or root two.

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Right.

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So we know that X equal to 16.

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Right.

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So for two is D.C. though if you subtract D.C. from AC, you're left with 80.

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So that's sixteen minus four or two.

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Now the next one is d.g.

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We have already found out d.g.

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That's Tooru two over here.

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Right.

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And the last one is D.C. That's what we need to find out.

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Let's write D.C. next.

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D.C. will be Boru to minus two.

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Right.

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We know that D.C. over here is four, too.

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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

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rule two.

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And these are our three answers.

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We have 80, which is equal to 16, minus four.

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Two we have D.G, which is Tooru two.

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And we have D.C., which is to route to.