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Question -

A circular park of radius 40 m is situated in a colony. Three boys Ankur, Amit and Anand are sitting at equal distance on its boundary each having a toy telephone in his hands to talk to each other. Find the length of the string of each phone.



Answer -

Since, AB = BC = CA. So, ABC is an equilateral triangle

Radius = OA = 40 m (Given)

We know, medians of equilateral triangle pass through thecircumcentre and intersect each other at the ratio 2 : 1.

Here AD is the median of equilateral triangle ABC, we can write:

OA/OD = 2/1

or 40/OD = 2/1

or OD = 20 m

Therefore, AD = OA + OD = (40 + 20) m = 60 m

Now, In ΔADC:

By Pythagoras theorem,

AC2 = AD2 + DC2

AC2 = 602 + (AC/2) 2

AC2 = 3600 + AC2 / 4

3/4 AC2 = 3600

AC2 = 4800

or AC = 40√3 m

Therefore, length of string of each phone will be 40√3 m.

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