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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=AO2−MO2=202−102 400 - 100 = 300 AM=√300 AS=2AM=2√300 =2×10√3=20√3

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