Ask a Doubt
Request a call back

Join NOW to get access to exclusive study material for best results

CBSE Class 9 Answered

on a circle's boundary 3 boys are standing equidistant from each other having a toy phone in hands to talk to each other.find the length of the phone's string if the radius of the circle is 20m.
Asked by | 04 Mar, 2013, 06:37: PM
answered-by-expert Expert Answer
Let A, B and C represent the 3 boys standing equidistant from one another on a circle's boundary. 
 
ABC form an equilateral triangle and the center of the circle O represents the circumcenter. 
Draw a perpendicular OM from point O to side AB of the triangle. 
 
Now, since a perpendicular from the center to a chord of a circle (i.e. AB here) bisects it. 
 
So, MB = MA = 1/2 AB
Now, in triangle MOB, angle OMB = 90 and hence, it is a right angled triangle.
 
Furthermore,in triangle AOB and triangle COB 
 
OB = BO (common)
AB = BC (sides of equilateral triangle)
AO = OC (radius)
triangle AOB is congruent to triangle COB  (By SSS)
hence, angle(OBA) = angle(OBC) (By CPCT)
 
Now, all angles of an equilateral triangle are equal to 60 degree. 
 
So, angle(OBA)+ angle(OBC) = 60
And since, they are equal, we get angle(OBA) = 30 degree. 
 
Now in triangle MOB 
using trignometry
 
MB = cos30 * OB
MB = sqrt(3)/2 * 20 = 10*sqrt(3)
Since, AB = 2*MB 
So, AB = 20sqrt(3) cm
 
So,the length of the phone string = 20sqrt(3) cm
Answered by | 05 Mar, 2013, 12:12: AM

Application Videos

Concept Videos

Multiple Choice Questions Practice Test
Answered Unanswered My Questions My Answers
CBSE 9 - Maths
if the diameter AD of a circle is 34 cm and the length of a chord AB is 30 cm. what is the distance of AB from the ce
Asked by indu.suresh1220 | 27 Dec, 2023, 11:12: PM
ANSWERED BY EXPERT ANSWERED BY EXPERT
CBSE 9 - Maths
prove that of all chords of circle through a given point within it, the chord which is bisected at that point is the smallest
Asked by subbusuchi1978 | 05 Nov, 2023, 10:24: AM
ANSWERED BY EXPERT ANSWERED BY EXPERT
CBSE 9 - Maths
if two circles intersect at two points prove that their centres lie in the perpendicular bisector of the common chord
Asked by rameshsonkar1234ramesh | 21 Dec, 2022, 11:03: PM
ANSWERED BY EXPERT ANSWERED BY EXPERT
CBSE 9 - Maths
AB is chord of a circle with centre O. Let P and T be two points on the circumpherence such that < APB # < ATB and < APB = 80 degree then what is the value of < ATB.
question image
Asked by sdmbotch1123 | 17 Dec, 2022, 09:39: PM
ANSWERED BY EXPERT ANSWERED BY EXPERT
CBSE 9 - Maths
prove that the median bisecting the hypotenuse of a right angled triangle is half of the hypotenuse
Asked by geetaradha8835 | 16 Dec, 2022, 07:59: PM
ANSWERED BY EXPERT ANSWERED BY EXPERT
CBSE 9 - Maths
solution
question image
Asked by rairai4971 | 11 Jun, 2022, 09:03: AM
ANSWERED BY EXPERT ANSWERED BY EXPERT
CBSE 9 - Maths
three girls Reshma Salma And Mandeep are playing a game by standing on a circle of radius 5 drawn in a park Reshma throws a ball to Salma Salma To mandip mandip to Reshma if the distance between Reshma and Salman and between Salman Mandeep 6 each what is the distance between Reshma Mandip
Asked by chalkekalyani80 | 06 Mar, 2022, 11:25: AM
ANSWERED BY EXPERT ANSWERED BY EXPERT
CBSE 9 - Maths
Prove that equal chords of a circle subtend equal angles at the centre.
Asked by sangeetabharti123456789 | 22 Feb, 2022, 09:01: AM
ANSWERED BY EXPERT ANSWERED BY EXPERT
CBSE 9 - Maths
What is a tangent?
Asked by manognareddy.p28 | 25 Jul, 2021, 12:52: PM
ANSWERED BY EXPERT ANSWERED BY EXPERT
CBSE 9 - Maths
Prove that the angle at the centre of a circle is twice the angle at the remaining part of the circle.
Asked by Samidhaindulkar133 | 11 Mar, 2021, 04:03: PM
ANSWERED BY EXPERT ANSWERED BY EXPERT
My Class Videos Tests ₹ Plans Ask a Doubt
Get Latest Study Material for Academic year 24-25 Click here
×