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Question

The area of a circle is A1, and the area of a regular pentagon inscribed in a circle is A2 . Then A1:A2 is
  1. None of these


Solution

The correct option is D


In a OAB, OA=OB=r
And AOB=360o5=72o
ar(OAB)=12.r.r.sin 72o=12.r2cos 18o
ar(pentagon)=52.r2 cos 18o
A1:A2=2πr25r2cos 18o=2π5secπ10

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