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Question

An equilateral triangle of side 9 cm is inscribed in a circle. The radius of the circle is 

(a) 3 cm

(b) 32 cm

(c) 33 cm

(d) 6 cm


Solution

ANSWER:
(c) 33 cm
Let ΔABC be an equilateral triangle of side 9 cm.
Let AD be one of its medians.
Then AD ⊥ BC and BD = 4.5 cm
AD2=AB2BD2

AD2=92(92)2

AD2=492924

AD2=3924

AD=932cm
Let G be the centroid of ΔABC.

Now, AD=AG+GD
Also, AG : GD = 2 : 1

  This means that AG=23AD or AG=23932cm or AG=33 cm

The radius of the circle is 33 cm

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