A circle is inscribed in a square, which is circumscribed by another circle.…
2025
A circle is inscribed in a square, which is circumscribed by another circle. If the diagonal of square is 2x, find the ratio of the area of the large circle to the area of the small circle ?
- A.
2:1
- B.
5:2
- C.
3:2
- D.
3:1
Attempted by 3 students.
Show answer & explanation
Correct answer: A
Given diagonal of the square = 2x.
The large circle passes through opposite vertices of the square, so its diameter equals the diagonal. Therefore the large circle radius R = x.
If the square side is s, then diagonal = s√2 = 2x, so s = 2x/√2 = x√2.
The small circle is inscribed in the square, so its diameter = s and its radius r = s/2 = (x√2)/2 = x/√2.
Area ratio (large : small) = πR² : πr² = R² : r² = x² : (x/√2)² = x² : (x²/2) = 2 : 1.
Answer: 2:1