Three boys, Ankur, Syed and David are sitting at equal distances on the boundary of a circular park of radius 20 m. Each of them has a toy telephone to talk to each other. Find the length of the string that connects the telephones of any two of the boys.
20√3
Let Ankur, Syed and David be denoted by A, S and D respectively in the circular park.
OS=OD=OA=20 m [Radius =20 m]
Construction: Draw OM⊥SA
Now, AS=SD=AD
So, △ASD is an equilateral triangle.
∠A=60∘
∠MAO=30∘
In △AMO
sin30∘=MOAO
⇒12=MOAO
⇒MO=AO2=202=10
Applying Pythagoras Theorem in △AMO:
AM2=AO2−MO2=202−102
=400−100=300
⇒AM=√300
⇒AS=2×AM=2√300
=2×10√3=20√3 m