1
You visited us 1 times! Enjoying our articles? Unlock Full Access!
Question

# 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.

Open in App
Solution

## It is given that AS = SD = DA Therefore, ΔASD is an equilateral triangle. The radius, OA = 20 m The medians of the equilateral triangle pass through the circumcentre (O) of the equilateral triangle ASD. We also know that medians intersect each other in the ratio 2:1. Let AB be the median of the equilateral triangle ASD, so we can write ⇒OAOB=21 ⇒20mOB=21 ⇒OB=(202)m=10m ∴AB=OA+OB=(20+10)m=30m In ΔABD, AD2=AB2+BD2[using pythagoras theorem] AD2=(30)2+(DS2)2 We have AS = SD = DA, ∴ AD2=(30)2+(AD2)2 AD2=900+14AD2 34AD2=900 AD2=1200 AD=20√3 Therefore, the length of the string of each phone will be 20√3m.

Suggest Corrections
3
Join BYJU'S Learning Program
Related Videos
Criteria for Similarity of Triangles
MATHEMATICS
Watch in App
Explore more
Join BYJU'S Learning Program