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,
AD2 = AB2 + BD2
AD2 = (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"`
