Question

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.

Answer 1

Given hat AB = BC = CA
So, ABC is an equilateral triangle
OA (radius) = 40m.
Medians of equilaterals triangles pass through the circum center (0) of the equilaterals
triangles ABC
We also know that median intersect each other at the 2 :1As AD is the median of equilaterals triangle ABC, we can write:
`(OA)/(OD)-2/7`
`⇒(40m)/(OD)-2/7`
`∴AD=OA+OD=(40+20)m`
`=60m`
In ΔADC
By using Pythagoras theorem

`AC^2=AD^2+DC^2`

`AC^2=AD^2+DC^2`
`AC^2=(60)^2+((AC)/2)^2`
`AC^2=3600+(AC^2)/4`

`⇒3/2AC^2=3600`\
`⇒AC^2=4800`
`⇒AC^2=40sqrt3m`

So, length of string of each phone will be `40sqrt3m`