Class 9 Exam  >  Class 9 Notes  >  RD Sharma Solutions for Class 9 Mathematics  >  RD Sharma Solutions -Ex-16.3, Circles, Class 9, Maths

Ex-16.3, Circles, Class 9, Maths RD Sharma Solutions | RD Sharma Solutions for Class 9 Mathematics PDF Download

Q1) Three girls Ishita, Isha and Nisha are playing a game by standing on a circle of radius 20m drawn in a park. Ishita throws a ball to Isha, Isha to Nisha and Nisha to Ishita. If the distance between Ishita and Isha and between Isha and Nisha is 24m each, what is the distance between Ishita and Nisha.

Solution:

Let R, S and M be the position of Ishita, Isha and Nisha respectively.

Ex-16.3, Circles, Class 9, Maths RD Sharma Solutions | RD Sharma Solutions for Class 9 Mathematics

AR = AS = Ex-16.3, Circles, Class 9, Maths RD Sharma Solutions | RD Sharma Solutions for Class 9 Mathematics = 12cm

OR = OS = OM = 20 cm                     [Radii of circle]

InΔOAR,

OA2+AR2 = OR2

OA2+122 = 202

OA2 = 400−144 = 256m2

OA = 16m

We know that, in an isosceles triangle altitude divides the base.

So in ΔRSM,∠RCS = 900 and RC = CM

Area of ΔORS = Ex-16.3, Circles, Class 9, Maths RD Sharma Solutions | RD Sharma Solutions for Class 9 Mathematics×OA×RS

Ex-16.3, Circles, Class 9, Maths RD Sharma Solutions | RD Sharma Solutions for Class 9 Mathematics×RC×OS = Ex-16.3, Circles, Class 9, Maths RD Sharma Solutions | RD Sharma Solutions for Class 9 Mathematics×16×24

⇒ RC×20 = 16×24

⇒ RC = 19.2

⇒ RM = 2(19.2) = 38.4m

So, the distance between Ishita and Nisha is 38.4m.

 

Q2) A circular park of radius 40 m is situated in a colony. Three boys Ankur, Amit and Anand 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 the string of each phone.

Solution:

Ex-16.3, Circles, Class 9, Maths RD Sharma Solutions | RD Sharma Solutions for Class 9 Mathematics

Given that AB = BC = CA

So, ABC is an equilateral triangle

OA (radius) = 40m

Medians of equilateral triangle pass through the circum centre (O) of the equilateral triangle ABC.

We also know that median intersect each other at the ratio 2 : 1.

As AD is the median of equilateral triangle ABC, we can write:

Ex-16.3, Circles, Class 9, Maths RD Sharma Solutions | RD Sharma Solutions for Class 9 Mathematics

Ex-16.3, Circles, Class 9, Maths RD Sharma Solutions | RD Sharma Solutions for Class 9 Mathematics

⇒ OD = 20m

Therefore, AD = OA + OD = (40 + 20) m

= 60 m

InΔADC

By using Pythagoras theorem

AC2 = AD2+DC2

AC2 = 602Ex-16.3, Circles, Class 9, Maths RD Sharma Solutions | RD Sharma Solutions for Class 9 Mathematics

AC2 = 3600+Ex-16.3, Circles, Class 9, Maths RD Sharma Solutions | RD Sharma Solutions for Class 9 Mathematics

Ex-16.3, Circles, Class 9, Maths RD Sharma Solutions | RD Sharma Solutions for Class 9 Mathematics = 3600

⇒ AC2 = 4800

⇒ AC = Ex-16.3, Circles, Class 9, Maths RD Sharma Solutions | RD Sharma Solutions for Class 9 Mathematics

So, length of string of each phone will be Ex-16.3, Circles, Class 9, Maths RD Sharma Solutions | RD Sharma Solutions for Class 9 Mathematics

The document Ex-16.3, Circles, Class 9, Maths RD Sharma Solutions | RD Sharma Solutions for Class 9 Mathematics is a part of the Class 9 Course RD Sharma Solutions for Class 9 Mathematics.
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FAQs on Ex-16.3, Circles, Class 9, Maths RD Sharma Solutions - RD Sharma Solutions for Class 9 Mathematics

1. What is the formula to find the circumference of a circle?
Ans. The formula to find the circumference of a circle is C = 2πr, where C represents the circumference and r represents the radius of the circle.
2. How do you find the area of a circle when the diameter is given?
Ans. To find the area of a circle when the diameter is given, you can use the formula A = πr^2, where A represents the area and r represents the radius. In this case, the radius can be found by dividing the diameter by 2.
3. How can I find the radius of a circle when only the circumference is given?
Ans. To find the radius of a circle when only the circumference is given, you can use the formula r = C/(2π), where r represents the radius and C represents the circumference.
4. Can the diameter of a circle be greater than the circumference?
Ans. No, the diameter of a circle cannot be greater than the circumference. The circumference is always greater than the diameter. In fact, the circumference is approximately 3.14 times the diameter, which is a mathematical constant known as pi (π).
5. Is it possible to find the area of a circle when only the circumference is given?
Ans. No, it is not possible to find the exact area of a circle when only the circumference is given. The area of a circle depends on the radius or diameter, not just the circumference. However, you can estimate the area using various approximation methods, such as dividing the circumference by 2π and then squaring the result.
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