Question

A circular park of radius 20m is situated in a colony. Three boys Ankur. Syed an
David are sitting at equal distance on its boundary each having a toy telephone
his hands to talk each other. Find the length of the string of each phone​

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 xmeters.

Draw AB⊥SD

∴SB=BD=21SD=2x m

In △ABS,∠B=90o

By Pythagoras theorem,

AS2=AB2+BS2

∴AB2=AS2−BS2=x2−(2x)2=43x2        

∴AB=23x m

Now, AB=AO+OB

OB=AB−AO

OB=(23x−20) m

In △OBS,

OS2=OB