A circular park of radius 20 m 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.

#### Solution

It is given that AS = SD = DA

Therefore, ΔASD is an equilateral triangle.

OA (radius) = 20 m

Medians of equilateral triangle pass through the circum centre (O) of the equilateral triangle ASD. We also know that medians intersect each other in the ratio 2: 1. As AB is the median of equilateral triangle ASD, we can write

`rArr(OA)/(OB) = 2/1`

`rArr(20m)/(OB) = 2/1`

`rArrOB=(20/2)m = 10m`

∴ AB = OA + OB = (20 + 10) m = 30 m

In ΔABD,

AD^{2} = AB^{2} + BD^{2}

AD^{2} = (30)^{2} + (AD/2)^{2}

`AD^2= 900 + 1/4AD^2`

`3/4AD^2 = 900`

`AD^2 = 1200`

`AD = 20sqrt3`

Therefore, the length of the string of each phone will be `20sqrt3" m"`