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# 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:**

It is given that

Diagonal of inner square = Diameter of circle = d

Consider x as the side of the inner square EFGH

In the right angled triangle EFG

Using the __Pythagoras theorem__

EG² = EF² + FG²

Substituting the values

d² = x² + x²

d² = 2x²

x² = d²/2

Area of inner square EFGH = x² = d²/2

Side of outer square ABCS = Diameter of circle = d

Area of outer square = d²

Therefore, the area of the outer square is not four times the area of the inner square.

**✦ Try This:** A square inscribed in a circle of diameter d and another square is circumscribing the circle. Show that the area of the outer square is four times the area of the inner square.

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

**NCERT Exemplar Class 10 Maths Exercise 11.2 Problem 3**

## 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

**Summary:**

In Fig 11.3, a square is inscribed in a circle of diameter d and another square is circumscribing the circle. The area of the outer square is not four times the area of the inner square

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