A circle is inscribed in a regular hexagon of side 2 under root 3 cm. Find the circumference of inscribed circle ?

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Answer 1 · 2018-07-02T04:28:21

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It is obvious from figure that

#"Radius of the circle"/"half the side of hexagon"=cot30^@#

#=>"Radius of the circle"/(1/2xx2/sqrt3)=sqrt3#

#=>"Radius of the circle"(r)=1# cm

So circumference of the inscribed circle #=2pir=2pi# cm

Answer 2 · 2018-07-02T08:22:58

#color(brown)("Circumference of the in-circle " = 2pi#

A regular hexagon will have six equilateral triangle with side equal to that of the hexagon.

Since the circle is inscribed with in the hexagon, radius of the in-circle is the height of the equilateral triangle #r = h#.

#"Given " OB = AB = OA = a = 2 / sqrt3#

#:. OM = r = h = (sqrt3 / 2 ) a = (sqrt3 / 2 ) * (2 / sqrt 3) = 1#

#"Circumference of the in-circle "= 2 pi r = 2 pi * 1 = 2pi#