CAT 1991 — QA Question 23
A circle is inscribed in a given square and another circle is circumscribed about the square. What is the ratio of the area of the inscribed circle to that of the circumscribed circle?
Answer & solution
Correct answer: 1 : 2
- A
2 : 3
- B
3 : 4
- C
1 : 4
1 : 2
As it is apparent from the following diagram, the diameter of the inscribed circle is equal to the side of the square, while the diameter of the circumscribed square is equal to the diagonal of the square.
Since the ratio of any two circles is equal to the ratio of the squares of their diameters, in this case the required ratio is equal to (side)2 : (diagonal)2
If the side of the square is a, its diagonal will be √2a
Now, the ratio of the side to the diagonal of a square = 1 : √2, the ratio of their squares will be 1 : 2.
Hence, option (d).