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  • In Figure, 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 Figure, 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.

Answers (1)

Solution

 

Diameter of circle = d

Side of biggest square = d

The area of the biggest square is = side × side   

=d \times d=d2

The diagonal of the smallest square = d

Let side = a

d2=a2+a2                 {using Pythagoras theorem}

d2=2a2

  \frac{d}{\sqrt{2}}=a

Area of the smallest square  \frac{d}{\sqrt{2}} \times \frac{d}{\sqrt{2}}=\frac{d^{2}}{2}

Here we found that the area of the outer square is not 4 times the area of the inner square.

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