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

Answer 1

LET A,B and C are the boys AND  AB, BC, AC are the strings of phones.

 O is the centre and COP is a line passing through centre and making a 90 degree angle with AB. Now AP = BP = x.

 And the line BO, bisects the angle ABC into two equal halves. So angle PBO is 30 degrees.

 Now  the right angled triangle PBO.

 In this Δ cos B = BP / BO

 i.e cos 30 = x / 20

 i.e x = 20 cos 30 = 17.32 m

 AS AP = BP = x,

 AB = 2x

 AB = 34.64 m

∴the length of each string is 34.64 m

Answer 2

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