Question 18

There is a circle of radius 1 cm. Each member of a sequence of regular polygons S1(n), n = 4,5,6,... , where n is the 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 the perimeters of the corresponding polygons of S1(n) and S2(n). Then $$\frac{L1(13)+2\pi }{L2(17)}$$ is

Solution

The perimeter of the circle is equal to 2$$\pi $$.

The perimeter of the polygon inscribing the circle is always greater than the perimeter of the circle => L1(13) > 2$$\pi $$

The perimeter of the polygon inscribed in the circle is always less than the perimeter of the circle => L2(13) < 2$$\pi $$

=> $$\frac{L1(13)+2\pi }{L2(17)}$$ > 2

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