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Question 6
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.

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Solution


It is given that AS = SD = DA
Therefore, ΔASD is an equilateral triangle.
The radius, OA = 20 m
The medians of the equilateral triangle pass through the circumcentre (O) of the equilateral triangle ASD.
We also know that medians intersect each other in the ratio 2:1.

Let AB be the median of the equilateral triangle ASD, so we can write
OAOB=21
20mOB=21
OB=(202)m=10m
AB=OA+OB=(20+10)m=30m

In ΔABD,
AD2=AB2+BD2[using pythagoras theorem]
AD2=(30)2+(DS2)2
We have AS = SD = DA,
AD2=(30)2+(AD2)2
AD2=900+14AD2
34AD2=900
AD2=1200
AD=203
Therefore, the length of the string of each phone will be 203m.

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