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Question

# 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.

A

20√3

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B

40√3

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C

30√3

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D

10√3

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Solution

## The correct option is A 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

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