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Let's do this question in the figure.

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The circle touches all the sides of a quadrilateral find.

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All right.

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Now pause the video, give it a try and then let's do it together.

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All right.

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We are back.

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I hope you have given it a try.

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Let's do it together.

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Now, over here, we have four points where the circle meets the given quadrilateral.

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Let's mark these points, SPQR.

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And it's OK.

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Now I can see that AP is equal to Pierce, right?

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Why is that?

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So these two are the engines from an exterior point to this circle, right?

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The point is the exterior point and A B and Eddie are the tangents.

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Right.

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And they are meeting the circular points.

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Therefore, it is equal to s let's call this distance X.

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So you have X over here and you have X over here.

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Similarly, you can see that over here you have White and Y, you're also there and Z and here over

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its end is right, because over here you can see BP and Peak.

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You are tandem's from an exterior point to the circle.

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Similarly, CQ and are tangent from an extra point to a circle and the Z and B.

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S are also tangent from an extra point to a circle.

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Right now over here, let's check what is A D plus B, C?

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That's 80 over here, which is seven and B, C, that's four centimetre.

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Now you can see that that's eleven centimetre.

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Right.

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And that's equal to X plus A plus Y plus Z.

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Right.

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All right, so that's equal to 11, because we know seven plus four is equal to 11.

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Now let's try what is a B plus KDDI?

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You will see that A B plus X plus why plus A plus Z, right.

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You have explosive way over here and a plus over here.

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We can see that these two are one and the same.

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Right.

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Therefore, this also has to be equal to 11 because we have 11 over here.

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So this also has to be 11 now A B plus KDDI has to be 11.

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And we know that AB is equal to eight.

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So eight plus KDDI is equal to 11.

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Right.

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Therefore, we get that is equal to three centimeter.

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And that is your answer.