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

It is given that AS = SD = DA

Therefore, ΔASD is an equilateral triangle.

OA (radius) = 20m

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 = 30m

In ΔABD,

AD² = AB² + BD² 

AD² = `(30)^2 + ((AD)/2)^2`

AD² = `900 + 1/4AD^2`

`3/4AD^2` = 900

AD² = 1200

AD = `20sqrt3`

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