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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