LIVE Course for free

Rated by 1 million+ students
Get app now
0 votes
201 views
in Circles by (28.2k points)
closed by

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.

1 Answer

+1 vote
by (27.8k points)
selected by
 
Best answer

Given that,

 AB = BC = CA 

So, 

ABC is an equilateral triangle 

OA = 40 cm (Radius) 

Medians of equilateral triangle pass through the circumference (O) of the equilateral triangle ABC 

We also know that, 

Median intersects each other at 2 : 1 as AD is the median of equilateral triangle ABC, 

We can write :

\(\frac{OA}{OD}\) \(\frac{2}{7}\) 

 \(\frac{40}{OD}\) \(\frac{2}{7}\) 

OD = 20 m

Therefore,

AO = OA + OD

= 40 + 20 

= 60 m

In Δ ADC,

By using Pythagoras theorem

AC2 = AO2 + DC2

AC2 = (60)2 + \((\frac{AC}{2})^2\) 

AC2 = 3600 + \(\frac{AC\,\times\,AC}{4}\) 

\(\frac{3}{4}\) AC2 = 3600

AC2 = 4800

AC = 40\(\sqrt 3\) m

So, 

Length of string of each phone will be  40\(\sqrt 3\) m.

Welcome to Sarthaks eConnect: A unique platform where students can interact with teachers/experts/students to get solutions to their queries. Students (upto class 10+2) preparing for All Government Exams, CBSE Board Exam, ICSE Board Exam, State Board Exam, JEE (Mains+Advance) and NEET can ask questions from any subject and get quick answers by subject teachers/ experts/mentors/students.

Categories

...