Question

A circular path of radius 20m situated in a Colony. Three boys Ankur, Syed and David sitting at equal distance on its boundary each having a toy telephone in has hand to talk each other. find the length of the string of each phone(class 9 ,circles ,NCERT)

Answer 1

Here's the ANSWER

Hope it helps .....

Answer 2

The total length of string is 60√3 m

1) Let Ankur, Syed and Colony be sitting on points A,B,C respectively and center of circle be O. Join lines OA,OB,OC. Let line OA meets BC on point D.

2) Given OA=OB=OC = 20 m.

3) Since,  AB = BC=CA, therefore point O will intersect the line AD in ratio 2:1

4) And OA = 20 m, therefore OD =10 m.

5) In triangle OBD, using Pythagoreas Theorem:

OB² = BD²+OD²

20² = BD² + 10²

BD = 10√3

6) In triangle BOD and COD,

OB = OC ( radius of circle)

OD = OD ( common side )

Angle ODB = Angle ODC ( 90°)

By, RHS congurency  BOD≅COD

Therefore BD = CD

7) BC = BD+CD = 2BD = 20√3

8) Total string length would be AB+BC+AC = 3BC = 60√3 m