# A circular park of radius 40 m is situated in a colony. Three boys Ankur, Amit and Anand are sitting at equal distance on its boundary

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A circular park of radius 40 m is situated in a colony. Three boys Ankur, Amit and Anand are sitting at equal distance on its boundary each having a toy telephone in his hands to talk to each other. Find the length of the string of each phone.

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Given that,

AB = BC = CA

So,

ABC is an equilateral triangle

Medians of equilateral triangle pass through the circumference (O) of the equilateral triangle ABC

We also know that,

Median intersects each other at 2 : 1 as AD is the median of equilateral triangle ABC,

We can write :

$\frac{OA}{OD}$ $\frac{2}{7}$

$\frac{40}{OD}$ $\frac{2}{7}$

OD = 20 m

Therefore,

AO = OA + OD

= 40 + 20

= 60 m

By using Pythagoras theorem

AC2 = AO2 + DC2

AC2 = (60)2 + $(\frac{AC}{2})^2$

AC2 = 3600 + $\frac{AC\,\times\,AC}{4}$

$\frac{3}{4}$ AC2 = 3600

AC2 = 4800

AC = 40$\sqrt 3$ m

So,

Length of string of each phone will be  40$\sqrt 3$ m.

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