An equilateral triangle is inscribed in a circle of radius 18 cm. Find the length of the triangle's side.


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Answer:

18√3 cm

Step by Step Explanation:
  1. ΔABC is inscribed in a circle. Lets O is the center of the circle.
  2. Now, connect all vertices of the triangle to O, and draw a perpendicular from O to 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.
     
    BD
    OB
      = cos30° =  
    √3
    2
     
    BD = OB ×  
    √3
    2
     
    = 18 ×  
    √3
    2
     
    = 9√3
  5. Therefore, BC = 2BD = 2(9√3) = 18√3 cm

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