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 take to each other. Find the length of the string of each phone.

Answer 1

As the three friends sitting at equal distance , that means the string form an equilateral triangle and the center of circle is the centroid of the triangle.
Let the side of the equilateral triangle be a units
then, by pythagoras theorem ,
the length perpendicular = a√3/2
and centroid divides the perpendicular in 2 :1 ratio.
so, radius = 2a√3/6
⇒20 = a/√3
⇒a = 20√3 m
length of string = 3× 20√3 = 60√3 m
                                          = 103.92 m 

Answer 2

Hi there!

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For solutions, Refer to the attached picture.
Regrets for handwriting _/\_

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Let's see some related topics :

⚫ Circle : The collection of all the points, which are at a fixed distance from a fixed point in a plane, is called a circle.

⚫ Radius : A line joining the centre to the Circumference of the circle, is called radius of a circle.

⚫ Secant : A line intersecting a circle at any two points, is called secant.

⚫ Diameter : A chord passing through the point of the circle, is called diameter. It is the longest chord.

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