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Q.

A circle is inscribed inside a regular pentagon and another circle is circumscribed about this pentagon. Similarly, a circle is inscribed in a regular heptagon and another circumscribed about the heptagon. The area of the regions between the two circles in two cases are A1
and A2, respectively. If each polygon has a side length of 2 units, then which one of the following is true ?

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a

A1=4925A2

b

A1=2549A2

c

A1=A2

d

A1=57A2

answer is D.

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Detailed Solution

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In first case  r=cotπ5;R=cosecπ5In second case  r1=cotπ7;R1=cosecπ711=πR2r2=πcosec3π5cot2π5=π
 

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M A2=πR12r12=πcosec2π7cot2π7=π A1=A2

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