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
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