Question

A circular park of radius 20m 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

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✨A circular park of radius 20m 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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✒ The length of the string of each phone is 20√3 m.

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⭐Solution :-

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=20m.

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°

By Pythagoras theorem,

AS² =AB² +BS²

∴AB² = AS²-BS²

${x}^{2} - ( \frac{x}{2} ) \: = \frac{3x}{4}$

∴ AB = $\sqrt{ \frac{3x}{2} }$

Now, AB=AO+OB

=> OB=AB−AO

=> OB=(√3x/2-20)m

In △OBS,

=> OS² =OB ²+SB²

=> 20² = (√3x/2-20)²+x/2²

=> 400 = 3/4x² +400-2(20)(√3x/2)+x²/4

=> 0 =x²-20√3x

∴ x=20√3 m

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Answer 2

Answer in the picture see