Question

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 each other. Find the length of the string of each phone.


[please answer this question ASAP with proper steps and explanation]
[perfect answer will receive a brainliest mark :)) ]​

Answer 1

Answer

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=21​SD=2x​ m

In △ABS,∠B=90o

By Pythagoras theorem,

AS2=AB2+BS2

∴AB2=AS2−BS2=x2−(2x​)2=43x2​        

∴AB=23

​x​ m

Now, AB=AO+OB

OB=AB−AO

OB=(23

​x​−20) m

In △OBS,

OS2=OB2+SB2

202=(23

​x​−20)2+(2x​)2

400=43​x2+400−2(20)(23

​x​)+4x2​

0=x2−203

​x

∴x=203

​m

The length of the string of each phone is 203

​m.