A circular park of 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 his hands to talk to each other. Find the length of the string of each phone.

Explanation

Let Ankur be represented as `A`, Syed as `S` and David as `D`.
The boys are sitting at an equal distance.
Hence, `/_\ASD` is an equilateral triangle.
Let the radius of the circular park be `r` meters.
`OS=r=20m.`
Let the length of each side of `/_\ASD` be `x` meters.
Draw `AB_|_SD`
`SB=BD=1/2SD=x/2m`
In`/_\ABS,/_B=90^@`
By Pythagoras theorem,`AS^2=AB^2+BS^2`
`AB^2=AS^2-BS^2`
`x^2−(x/2)^2=3x^2/4`
`AB=(sqrt3x)/2m`
Now,`AB=AO+OB`
`OB=AB−AO`
`OB=(sqrt3x/2−20)m`
In`/_\OBS,OS^2=OB^2+SB^2`
`20^2=((sqrt3x)/2-20)^2+(x/2)^2`
`400=3/4​x^2+400−2(20)(sqrt3x)/2)+x^2/4`
`0=x^2−20sqrt3x`
`x=20sqrt3m`
The length of the string of each phone is `20sqrt3m`.