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Q.

A regular hexagon & a regular dodecagon are inscribed in the same circle. If the side of the dodecagon is 3-1, then the side of the hexagon is ____ unit.


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Detailed Solution

the side of the dodecagon is 3-1.
the angle made at center by the sides of a regular dodecagon is 360∘12=30∘.
sin15∘=3-12r
⇒3-122=3-12r
⇒r=2
  
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