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?
- 2 : 3
- 3 : 4
- 1 : 2
- 1 : 4
Let a be the side of the square.
The side of the square will be the diameter of the inscribed circle.
Radius of inscribed circle = a/2
Area of inscribed circle = π(a/2)2 = 1/4 a2π
The diagonal of the square will be the diameter of the circumscribed circle.
Radius of circumscribed circle = √2a/2
Area of circumscribed circle = π(√2a/2)2 = 1/2 a2π
The ratio of the area is 1 : 2
The correct option is C.