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Question

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

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Solution

A is the position of Ankur.

B is the position of Syed.

C is the position of David.

In the equilateral triangle ABC, altitude, median, and angle bisector are all same.

OB bisects B [ OB is the angle bisector]

OBD=602=30

In ΔOBD,cos30=BDOB=a2R [R=20 m= radius of the circle]

a=2Rcos30

a=2×20×32=203m [cos30=32 ]

Hence, the length of the string is 203 m


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