An equilateral triangle with a side of length 6√3 cm is inscribed in a circle. Find the radius of the circle.


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Answer:

6 cm

Step by Step Explanation:
  1. ΔABC is inscribed in a circle. Let O be the center of the circle.
  2. Now, connect all vertices of the triangle to O, and draw a perpendicular from O meet the side BC of the triangle at point D.
  3. We know, all the angles of an equilateral triangle measure 60°.
    So, angle ACB = ABC = CBA = 60°
    OB and OC are bisectors of ∠B and ∠C respectively,
    ∠OBD = 30°
  4. Since, triangle ODB is a right- angled triangle.
    We have,
     
    BD
    OB
      = cos 30° =  
    √3
    2
     
    OB =  
    BD
     
    √3
    2
     
     
    =  
    3√3
     
    √3
    2
     
     
    = 6 cm
  5. Therefore, the radius of the circle is 6 cm.

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