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.​

Answer 1

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=

2

1

SD=

2

x

m

In △ABS,∠B=90

o

By Pythagoras theorem,

AS

2

=AB

2

+BS

2

∴AB

2

=AS

2

−BS

2

=x

2

−(

2

x

)

2

=

4

3x

2

∴AB=

2

3

x

m

Now, AB=AO+OB

OB=AB−AO

OB=(

2

3

x

−20) m

In △OBS,

OS

2

=OB

2

+SB

2

20

2

=(

2

3

x

−20)

2

+(

2

x

)

2

400=

4

3

x

2

+400−2(20)(

2

3

x

)+

4

x

2

0=x

2

−20

3

x

∴x=20

3

m

The length of the string of each phone is 20

3

m.

solution