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# In Fig. 11.2, a circle is inscribed in a square of side 5 cm and another circle is circumscribing the square. Is it true to say that area of the outer circle is two times the area of the inner circle? Give reasons for your answer

**Solution:**

Given, a __circle__ is inscribed in a side of square 5 cm

Another circle is circumscribing the __square__.

We have to determine if the area of the outer circle is two times the area of the inner circle.

Side of square = diameter of inscribed circle i.e., inner circle

So, diameter of inner circle = 5 cm

Radius = 5/2 cm

__Area of circle__ = πr²

Area of inner circle = π(5/2)²

= 25π/4 square cm

__Diagonal of square__ = diameter of outer circle

Area of square = 5(5) = 25 square cm

__Area of square__ = (diagonal)²/2

25 = diagonal²/2

Diagonal² = 25(2)

Diagonal² = 50

Taking square root,

Diagonal = 5√2 cm

So, Diameter of outer circle = 5√2 cm

Area of outer circle = π(5√2/2)²

= 50/4π

= 25π/2

Area of outer circle = 2(area of inner circle)

25π/2 = 2(25π/4)

25π/2 = 25π/2

Therefore, the area of the outer circle is two times the area of the inner circle.

**✦ Try This:** A circle is inscribed in a square and the square is circumscribed by another circle. What is the ratio of the areas of the inner circle to the outer circle?

**☛ Also Check: **NCERT Solutions for Class 10 Maths Chapter 12

**NCERT Exemplar Class 10 Maths Exercise 11.2 Sample Problem 2**

## In Fig. 11.2, a circle is inscribed in a square of side 5 cm and another circle is circumscribing the square. Is it true to say that area of the outer circle is two times the area of the inner circle? Give reasons for your answer

**Summary:**

In Fig. 11.2, a circle is inscribed in a square of side 5 cm and another circle is circumscribing the square. It is true to say that the area of the outer circle is two times the area of the inner circle

**☛ Related Questions:**

- Is the area of the circle inscribed in a square of side a cm, πa² cm²? Give reasons for your answer
- Will it be true to say that the perimeter of a square circumscribing a circle of radius a cm is 8a c . . . .
- In Fig 11.3, a square is inscribed in a circle of diameter d and another square is circumscribing th . . . .

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