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Question -

A circular park of radius 20m is situated in a colony. Three boysAnkur, Syed and David are sitting at equal distance on its boundary each havinga toy telephone in his hands to talk each other. Find the length of the stringof each phone.



Answer -

First, draw a diagramaccording to the given statements. The diagram will look as follows.

Here the positions ofAnkur, Syed and David are represented as A, B and C respectively. Since theyare sitting at equal distances, the triangle ABC will form an equilateraltriangle.

AD ⊥ BC is drawn. Now, AD is median of ΔABC and itpasses through the centre O.

Also, O is thecentroid of the ΔABC. OA is the radius of the triangle.

OA = 2/3 AD

Let the side of atriangle a metres then BD = a/2 m.

Applying Pythagorastheorem in ΔABD,

AB2 =BD2+AD2

⇒ AD2 =AB2 -BD2

⇒ AD2 =a2 -(a/2)2

⇒ AD2 =3a2/4

⇒ AD = √3a/2

OA = 2/3 AD

20 m = 2/3 × √3a/2

a = 20√3 m

So, the length of thestring of the toy is 20√3 m.

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