Question

An equilateral triangle of side 9cm is inscribed in a circle. Find its radius

Answer 1

Plz look into the diagram for details

Given: triangle ABC is equilateral

                  Thus, <ABC =60°

                             AB=9cm

Sol: AD divides BC into half

       So, BD+DC=BC

             2BD = 9cm

                 BD=9/2 =4.5cm

     

          <OBD=30°

           

              In triangle OBD,

                  Cos30°= BD/BO

                     Cos30°=4.5/BO

                     Root3/2 =4.5/BO

                     BO = 4.5×2/root3

                      BO= 9/root 3

                       BO=3× root3×root3/root3

                     BO = 3root3

Hence radius =3×root3