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Question

A circular park of radius20m 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 talk each other. Find the length of the string of each phone.


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Solution

The positions of Ankur, Syed and David are represented as A,B&C respectively.

As they are sitting at equal distances, the triangle is equilateral

ADBC is drawn.

ADis the median of ΔABCand it passes through the centre O.

Ois the centroid of the ΔABC.

OAis the radius of the triangle.

OA=23AD

Let the side of a triangle a metres thenBD=a2

On applying Pythagoras theorem in ΔABD,

=AB2=BD2+AD2AD2=AB2-BD2AD2=a2-a22AD2=3a24AD=32Therefore,OA=23AD20m=23×3a2a=203m

Hence , the length of the string of the toy is 203m


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