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Let's do this question in the figure is equal to 20 centimeter BQ is to cure is to ask you is equal

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to three is to do is to one answer is the angle by sector of angle T.

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S Q This angle over here.

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All right.

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Find the inner radius of triangle B askew.

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This triangles in radius is what we need to find.

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All right.

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Was the video.

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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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Let's do it together.

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Let's mark the information that is given in the question piece is equal to twenty centimeter and P Q

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is too curious to ask you is three is to do is to one.

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Therefore I can write because three x Q R as two X and ask you as X.

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Alright now over here we have an external angle by sector.

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Remember to write the ratios correctly.

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Imagine that it's an internal angle by sector.

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Right.

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So imagine as far as the internal angle by sector then we know that the ratio is pIace by SKU is equal

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to P R by our Q right.

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So let's write that over here because my skill is equal to PR by our Q And now we remove the imagination

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that this is an internal angle by sector.

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So we are back and we have the required ratio return correctly.

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Now let's plug in the values we know P as is equal to twenty askew is equal to x p, r is three X plus

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two weeks and argue that's two X.

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So let's write the values.

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Twenty by X is equal to three X plus two weeks by two X that is twenty by X is equal to five by two

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or on simplifying you get X is equal to four in the two or eight.

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So let's write the sides of this triangle over here.

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We have the sides of triangle be as good as twenty, twenty four and eight.

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Alright so what is the semi perimeter.

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That's twenty plus twenty four plus eight which is fifty two.

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Divided by two.

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Right.

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The semi perimeter is fifty two by two which gives you twenty six.

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All right.

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Now as per her own formula, what is the area of triangle bascule that's square root of S into S minus

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E in the S minus B into S minus C.

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Right.

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So that's equal to square root of twenty six into six in the two in the eighteen.

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Right to S is twenty six S minus eight.

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So S minus twenty six, twenty six minus twenty four gives you two and twenty six, minus eight gives

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you eighteen.

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So these are the values over here, Bergeron's formula.

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So on solving this you will get the area as twelve root thirty nine.

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Now we know that the area also can be found as the product of the in radius and the semi perimeter that's

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our into S and that is equal to R into twenty six, therefore twelve root thirty nine is equal to are

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in the twenty six or eight is equal to twelve root thirty nine by twenty six or it simplifies as.

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Six RWD thirty nine divided by 13, and that is your answer.