what is the tricky way for solving the question of class 9^{th} ncert math of Circles chapter of ncert of exercise 10.4 of math give me the best and simple way for solving this question in easy way of question no. 6 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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# 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. Q.6

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First, draw a diagram according to the given statements. The diagram will look as follows.

Here the positions of Ankur, Syed and David are represented as A, B and C respectively. Since they are sitting at equal distances, the triangle ABC will form an equilateral triangle.

AD âŠ¥ BC is drawn. Now, AD is median of Î”ABC and it passes through the centre O.

Also, O is the centroid of the Î”ABC. OA is the radius of the triangle.

OA = 2/3 AD

Let the side of a triangle a metres then BD = a/2 m.

Applying Pythagoras theorem in Î”ABD,

AB

^{2 }= BD^{2}+AD^{2}â‡’ AD

^{2 }= AB^{2 }-BD^{2 }â‡’ AD

^{2 }= a^{2 }-(a/2)^{2}â‡’ AD

^{2 }= 3a^{2}/4â‡’ AD = âˆš3a/2

OA = 2/3 AD

20 m = 2/3 Ã— âˆš3a/2

a = 20âˆš3 m

So, the length of the string of the toy is 20âˆš3 m.