Question

There is a circle of radius 1 cm. Each member of a sequence of regular polygons S1(n), n = 4, 5, 6, ... where n = number of sides of the polygon, is circumscribing the circle and each member of the sequence of regular polygons S2(n), n = 4, 5, 6, ... where n is the number of sides of the polygon, is inscribed in the circle. Let L1(n) and L2(n) denote perimeters of the corresponding polygons of S1(n) and S2(n). Then $\angle L1(13) + 2\pi$ is L2(17) is:

• A. Greater than $\pi/4$ but less than 1
• B. Greater than 1 and less than 2
• C. Greater than 1 and less than 2
• D. Less than $\pi/4$

Hint:

When dealing with sequences involving polygons inscribed and circumscribed in a circle, carefully calculate each step using known geometric formulas for perimeters and angles.

Answer 1

The Correct Option is B

We can calculate the perimeters of the inscribed and circumscribed polygons and then use the given condition to evaluate the angles. The correct option is (2) where the angle falls between 1 and 2.