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प्रश्न
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.
उत्तर
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.
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