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Question

# A circular park with radius 20m 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 this hands to talk each other. The length of the string of each phone is

A
20m
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B
17.32m
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C
34.64m
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D
30m
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Solution

## The correct option is D 34.64mLet us denote the positions of Ankur as A, that of Syed as S and that of David as DSo, AS=SD=DA. ∴ΔASD is an equilateral triangle.Let the centre of the park be O.Then, we have a circle circumscribing an equilateral △ASD, the radius being OA=20m. The length of the telephone wire= AS=SD=DA. AO is joined and is produced to meet DS at N.Now, we know that the centriod of an equilateral triangle coincides with the centre of its circumcircle and the median of the triangle contains the radius.∴AN is the median as well as the height of ΔASD and O is the centroid of ΔASD. So, AN=32OA=32×20m=30m(OA:ON=2:1, when O is the centroid and AN=OA+ON is the median of any triangle). Now, side a of an equilateral triangle =2×height√3. Here, a=AS=SD=DA=2×30√3m=20√3m=34.64m.

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