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.

Answer 1

Data: 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. 

To Prove: Length of wire of telephone = ? 

Proof: In this figure, AS = SD = DA 

∴ ASD is an equilateral triangle. 

∴ OA = 20 m. 

(∵ radius) Median passed through centre of circle. 

∴ AB is the median. AD⊥SD 

Median of equilateral triangle divides in the ratio 2 : 1 in the centre? 

∴ AO : OB = 2 : 1