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


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 situation of Ankur, Syed and David be A, S and D respectively in the circular path.

OS = OD = OA = 20m

construction: Draw OM SA

Now, AS = SD = AD

So, ASD is an equilateral triangle.

A=60

MAO=30

MO=AO2

[In right angled triangle, the side opposite to 30 is half of hypotenuse]

MO=202=10

AM2=AO2MO2=202102

400 - 100 = 300

AM=300

AS=2AM=2300

=2×103=203


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