A circular park of radius $ 20 \mathrm{~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 hands to talk each other. Find the length of the string of each phone.

Given:

A circular park of radius \( 20 \mathrm{~m} \) is situated in a colony. Three boys Ankur, Syed and David are sitting at an equal distance on its boundary each having a toy telephone in his hands to talk to each other.

To do:

We have to find the length of the string of each phone.

Solution:

The radius of the circular park $= 20\ m$

Ankur, Syed and David are sitting at equal distance to each other.

By joining the points, an equilateral triangle $ABC$ is formed.

Produce $BO$ to $L$ which is the perpendicular bisector of $AC$.

Therefore,

$BL = 20 + 10$

$= 30\ m$              ($O$ is the centroid of $\triangle ABC$)

Let $a$ be the side of $\triangle ABC$

$\Rightarrow \frac{\sqrt{3}}{2} a=30$

$a=\frac{30 \times 2}{\sqrt{3}}$

$a=\frac{60 \times \sqrt{3}}{\sqrt{3} \times \sqrt{3}}$

$a=\frac{60 \times \sqrt{3}}{3}$

$a=20 \sqrt{3} \mathrm{~m}$

Hence the distance between each other is $20\sqrt3\ m$.  

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Updated on: 10-Oct-2022

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