Question

(24) 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.

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Answer 1

Answer:

Given:- Circular park with radius 20m. 

Let Ankur Syed and David be donated by points A,S&D respectively. Given all there are sitting at equal distance i.e AS=SD=AD

To find: Length of AS=SD=AD

Explanation: LEt AS=SD=AD=2x   [Ref. image 1]

In ASD, all sides are equal,

∴ASD is equilateral triangle 

We draw OP⊥SD           (perpendicular drawn from centre of circle to a chord of the chord)

So, SP=DP=21SD [Ref. image 2]

⇒SP=DP=22x=x

Join  OS & AO

In ΔOPS

By Pythagoras theorem 

OS2=OP2+PS2

(20)2=OP2+x2

(400)=OP+x2

400−x2=OP2

OP=400−x2

In △APS

By Pythagoras theorem

AS2=AP2+PS2

(2x)2=AP2+x2

$$4x^2 = AP^2+x^2

4x2−x