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Home » In Fig 11.3, a square is inscribed in a circle of diameter d and another square is circumscribing the circle. Is the area of the outer square four times the area of the inner square? Give reasons for your answer.
In Fig 11.3, a square is inscribed in a circle of diameter d and another square is circumscribing the circle. Is the area of the outer square four times the area of the inner square? Give reasons for your answer.
Areas Related to Circles | Exercise 11.2 | Maths | NCERT Exemplar
In Fig 11.3, a square is inscribed in a circle of diameter d and another square is circumscribing the circle. Is the area of the outer square four times the area of the inner square? Give reasons for your answer.

Solution:

The given statement is False

Explanation:

From the fig, Let the Diameter of the circle = d

Therefore,

Diagonal of inner square (EFGH) = Side of the outer square (ABCD) = Diameter of circle = d

Let  us take  side of inner square EFGH be a

Now assume EFG is a right angled triangle,

Then,

    \[{{(EG)}^{2}}={{(EF)}^{2}}+{{(FG)}^{2}}\]

By Pythagoras theorem)

i.e., 

    \[{{d}^{2}}={{a}^{2}}+{{a}^{2}}\]

⇒ 

    \[{{d}^{2}}=2{{a}^{2}}\]

⇒ 

    \[{{a}^{2}}={{d}^{2}}/2\]

Therefore, Area of inner circle =

    \[{{a}^{2}}={{d}^{2}}/2\]

Also, Area of outer square (ABCD) =

    \[{{d}^{2}}\]

Therefore, the area of the outer circle(ABCD) is only two times the area of the inner circle(EFGH).

Thus, the given statement is false.

 

i

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