Question

EXAMPLE 12 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 to
each other. Find the length of the string of each phone.
[NCERT)
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Answer 1

Answer:

Step-by-step explanation:

Let Ankur be represented as A, Syed as S and David as D.

The boys are sitting at an equal distance.

Hence, △ASD is an equilateral triangle.

Let the radius of the circular park be r meters.

∴ OS=r=20 m,

Let the length of each side of △ASD be x meters.

Draw AB⊥SD,

∴SB=BD=  1/2 SD=x/2 m,

⇒In △ABS,∠B=90

O,

⇒By Pythagoras theorem,

⇒AS²=AB²+BS²,∴AB²=AS²-BS²=x²-(x/2)²=3x²/4,∴AB=√3x/2 m.

⇒Now, AB=AO+OB ,

⇒OB=AB−AO ,

⇒OB=(√3x/2-20)m,

⇒In △OBS,

⇒ OS²=OB²+SB²,

⇒20²,

⇒(√3x/2-20)²+(x/2)²,

⇒400=3/4 x²+400-2(20)(√3x/2)+x²/4,

⇒0=x²-20√3x,

⇒x=20√3 m,

The length of the string of each phone is 20√3m.

Hope it helps.✔✔✔

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Answer 2

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