Question:
The figure below shows 2 concentric circles with centre O. PQRS is a square inscribed in the outer circle. It also circumscribes the inner circle touching it at points B, C, D and A. What is the ratio of the perimeter of the outer circle to that of the polygon ABCD?
The figure below shows 2 concentric circles with centre O. PQRS is a square inscribed in the outer circle. It also circumscribes the inner circle touching it at points B, C, D and A. What is the ratio of the perimeter of the outer circle to that of the polygon ABCD?
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For geometric problems involving inscribed and circumscribed figures, use the properties of the figures to derive relationships between their dimensions.
Updated On: Aug 5, 2025
- $\pi/4$
- $3\pi/2$
- $\pi/2$
- $\pi$
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The Correct Option is C
Solution and Explanation
We first calculate the perimeter of the square PQRS and then use the geometry of the concentric circles to calculate the ratio of the perimeter of the outer circle to the perimeter of the polygon ABCD.
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