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 string of each phone

Solution:

Centre and Centroid are the same for an equilateral triangle, and it divides the median in the ratio 2 : 1.

Let A, D, S denote the positions of Ankur, David, and Syed, respectively.

∆ADS is an equilateral triangle since all the 3 boys are equidistant from one another.

Let B denote the mid-point of DS, and hence AB is the median and perpendicular bisector of DS.

Hence ∆ABS is a right-angled triangle with ∠ABS = 90º.

O (centroid) divides the line AB in the ratio 2 : 1. So OA : OB = 2 : 1.

OA/OB = 2/1

Since OA = 20 (given)

thus, OB = 10m

AB = OA + OB = 20 + 10 = 30 m ….(1)

Let the side of the equilateral triangle ∆ADS be 2x.

AD = DS = SA = 2x …. (2)

Since B is the mid-point of DS, we get BS = BD = x …. (3)

Applying Pythagoras theorem to ∆ABD, we get:

AD² = AB² + BD²

(2x)² = 30² + x²

4x² = 900 + x²

3x² = 900

x² = 300

x = 10√3

x = 17.32

AD = DS = SA = 2x = 34.64 m

Length of the string = Distance between them = AD or DS or SA = 34.64 m.

☛ Check: NCERT Solutions for Class 9 Maths Chapter 10

---

Video Solution:

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

Maths NCERT Solutions Class 9 - Chapter 10 Exercise 10.4 Question 6:

Summary:

If a circular park of radius of 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 to each other, then the length of the string of each phone is 34.64m.

---

☛ Related Questions:

• If two equal chords of a circle intersect within the circle, prove that the segments of one chord are equal to corresponding segments of the other chord.
• If two equal chords of a circle intersect within the circle, prove that the line joining the point of intersection to the center makes equal angles with the chords.
• If a line intersects two concentric circles (circles with the same center) with center O at A, B, C and D, prove that AB = CD.
• Three girls Reshma, Salma and Mandip are playing a game by standing on a circle of radius 5m drawn in a park. Reshma throws a ball to Salma, Salma to Mandip, Mandip to Reshma. If the distance between Reshma and Salma and between Salma and Mandip is 6m each, what is the distance between Reshma and Mandip?