Question

The side of a regular dodecagon is 2 cm. The radius of the circumscribed circle in cms ?

Answer 1

Regular Dodecagon has 12 sides.  The external angle = 360/12 = 30°
The internal angle = 150°.

If we join one side AB with center O, then AO=BO= Circumradius = R.
ΔABO is isosceles.   Angle between two radii AO & BO = 30°  .  We apply cosine rule.

   a^2 = R^2 + R^2 - 2 R * R * cos30°
          =   R^2 ( 2 - √3)

   R = a √(2+√3) = 3.863 cm

Answer 2

LISTEN TO YOUR CLASS

Regular Dodecagon has 12 sides.  The external angle = 360/12 = 30°

The internal angle = 150°.

If we join one side AB with center O, then AO=BO= Circumradius = R.

ΔABO is isosceles.   Angle between two radii AO & BO = 30°  .  We apply cosine rule.

  a^2 = R^2 + R^2 - 2 R * R * cos30°

         =   R^2 ( 2 - √3)

  R = a √(2+√3) = 3.863 cm