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

Let the points at which the boys are sitting be A, B and C
Circle has the center O

Now Since the boys are sitting at equal distance thus ABC is an equilateral triangle formed inside the circle

Thus radius
                OA = OB = OC = 20 m

Since it is an equilateral traingle
Thus each angle is 60 deg

In triangle OAB

Angle OAB = Angle OBA = 60/2 = 30 deg
Angle AOB = 120 deg
Drwaing a perpendicular from on AB at D
we get Angle ODB = 90 deg
Thus in triangle ODB
Sin 60 deg = BD/OB
root3/2 = BD/20
BD = 10root3
Thus 
          AB = 20 root3 = BC = AC
So length of string = 20 root3 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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Thanks for the question !

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