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.

Academic Mathematics NCERT Class 9

Given:

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.

To do:

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

Solution:

Radius of the circular park $= 40\ m$

Ankur, Amit and Anand are sitting at equal distance to each other.

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

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

Therefore,

$BL = 40 + 20$

$= 60\ m$ ($O$ is the centroid of $\triangle ABC$)

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

$\Rightarrow \frac{\sqrt{3}}{2} a=60$

$a=\frac{60 \times 2}{\sqrt{3}}$

$a=\frac{120 \times \sqrt{3}}{\sqrt{3} \times \sqrt{3}}$

$a=\frac{120 \times \sqrt{3}}{3}$

$a=40 \sqrt{3} \mathrm{~m}$

Hence the distance between each other is $40\sqrt3\ m$.

Updated on: 10-Oct-2022

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