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A circular park of radius 20m is situated in a colony . Three boys Ankur, Syed and David are sitting at equal distance on its boundary each having a toy

telephone in his hands to take to each other. Find the length of the string of each phone.


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As the three friends sitting at equal distance , that means the string form an equilateral triangle and the center of circle is the centroid of the triangle.
Let the side of the equilateral triangle be a units
then, by pythagoras theorem ,
the length perpendicular = a√3/2
and centroid divides the perpendicular in 2 :1 ratio.
so, radius = 2a√3/6
⇒20 = a/√3
a = 20√3 m
length of string = 3× 20√3 = 60√3 m
                                          = 103.92 m 
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