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

cos B = BP / BO

 that is cos 30 = x / 20

 that is x = 20 cos 30 = 17.32 m

 Since AP = BP = x,

 AB = 2x

 AB = 34.64 m

 So the length of each string is 34.64 m

Answer 2

hey!

let AB,BC,AC be the length of each string

AB=BC=AC [ equal arcs subtends equal chords]

construction : draw perpendicular bisector of AB,BC,AC

•AO=OB=OC(equal radii)=20m

Centroid - the centroid of a circle is the point located at 2/3 of the distance from the vertex along a median

AO/OD=2/1 [centroid of a circle divides a median in the ratio of 2:1

20/OD=2/1
20/2 = OD
10m=OD

in∆BOD
(BD)^2=(20)^2-(10)^2
BD=√400-100
BD=√300
BD=10√3

a line from a centre to the chord is the perpendicular bisetcor of the chord

BD=DC

BC=2×10√3=20√3m

AB=BC=CA=20√3m

hence length of each string are 20√3m