3 boys Ankur, Syed and David are sitting at equal distances on the boundary of a circular park of radius 20m. Each of them has a toy telephone to talk to each other. Find the length of the string that connects the telephones of any two of the boys.
20√3
Let Ankur, Syed and David be denoted by A, S and D respectively in the circular park.
OS = OD = OA = 20m
construction: Draw OM ⊥ SA
Now, AS = SD = AD
So, ASD is an equilateral triangle.
∠A = 60∘
∠MAO = 30∘
MO = AO2
[In right angled triangle, the side opposite to 30∘ is half of hypotenuse]
MO = 202 = 10
AM2 = AO2 - MO2 = 202 - 102
400 - 100 = 300
AM = √300
AS = 2 AM = 2 √300
= 2 × 10√3 = 20√3