- RD Sharma Solutions for Class 6 Maths Chapter 14 Circles
- RD Sharma Solutions for Class 6 Chapter 14 Circles - Download PDF
- RD Sharma Solutions Class 6 Maths Chapter 14 Circles - Objective Type
- Advanced Practice Questions – Chapter 14 Circles (With Detailed Solutions)
- RD Sharma Solutions for Class 6 Maths Chapter 14 Circles FAQs
RD Sharma Solutions for Class 6 Maths Chapter 14 Circles
Chapter 14 of RD Sharma Class 6 Maths introduces students to one of the most fundamental and fascinating shapes in geometry — the circle. This chapter builds a strong base in understanding the parts and properties of circles, setting the stage for more advanced geometric concepts in higher classes. Students are introduced to important terms such as radius, diameter, chord, arc, circumference, sector, and segment, along with practical applications of circles in daily life.
The chapter also covers how to draw circles using a compass, how to identify symmetrical properties, and recognize concentric circles. This foundation helps learners visualize and relate to real-world objects like wheels, clocks, coins, and plates — all of which are circular in shape.
RD Sharma Solutions for Class 6 Maths Chapter 14 Circles
RD Sharma Solutions for Class 6 Maths provide a comprehensive and student-friendly approach to mastering mathematical concepts. With step-by-step explanations and a variety of solved examples, RD Sharma Solutions for Class 6 Maths make complex problems easy to understand and practice, making them an ideal resource for exam preparation and daily learning.
Understanding RD Sharma Solutions for Class 6 Maths Chapter 14 Circles not only enhances visual-spatial reasoning but also strengthens the geometric base required for higher classes, especially in topics like mensuration, coordinate geometry, and construction. A clear grasp of this chapter will help students tackle more complex problems involving perimeters, areas, tangents, and trigonometric applications in later grades.
Topics Covered in Class 6 Maths Chapter 14 – Circles
- Definition and basic parts of a circle (centre, radius, diameter, chord, etc.)
- The relationship between radius and diameter
- Concepts of arc, semicircle, and full circle
- Drawing a circle with a compass
- Understanding interior and exterior of a circle
- Identifying symmetrical aspects of a circle
- Simple construction and identification-based problems
RD Sharma Solutions for Class 6 Chapter 14 Circles - Download PDF
We’ve provided step-by-step RD Sharma Solutions for Class 6 Maths Chapter 14 in a simple, clear, and easy-to-understand format. These solutions follow the latest CBSE curriculum and are tailored to help students practice, revise, and gain confidence.
The downloadable PDF format makes it convenient for students to access solutions offline and learn at their own pace. By practicing regularly with these well-structured answers, students can develop a strong conceptual understanding and improve accuracy in solving geometry problems.
Exercises Covered in RD Sharma Chapter 14 – Circles
The chapter is divided into the following exercises, each focusing on a specific aspect of circles:
- Exercise 14.1 – Understanding key terms and definitions
- Exercise 14.2 – Drawing and identifying parts of a circle
- Exercise 14.3 – Solving conceptual problems based on radius, diameter, and chords
- Exercise 14.4 – Interior and exterior points of a circle
Each exercise contains a mix of objective-type questions, diagram-based identification tasks, and short-answer problems that reinforce learning effectively.
RD Sharma Solutions Class 6 Maths Chapter 14 Circles - Objective Type
1. What is the maximum number of equal-length chords that can pass through the center of a circle?
A) 1
B) 2
C) Infinite
D) None
Answer: C) Infinite
Explanation: Any number of chords of equal length can pass through the center if they all form diameters at different angles.
2. Which of the following statements is always true for a circle?
A) All diameters are equal, but all radii are not
B) All radii are equal, but all diameters are not
C) All radii and diameters are equal in length respectively
D) A circle has no radius
Answer: C) All radii and diameters are equal in length respectively
Explanation: All radii in a circle have the same length from the center to the boundary, and all diameters are twice the radius.
3. What is the relationship between a radius and a diameter?
A) Radius = Diameter
B) Radius = Diameter ÷ 2
C) Radius = Diameter × 2
D) Radius = Circumference
Answer: B) Radius = Diameter ÷ 2
4. In a circle, the longest chord is always the —
A) Radius
B) Arc
C) Diameter
D) Chord that doesn't pass through the center
Answer: C) Diameter
5. If a circle has a radius of 5 cm, what is the length of the diameter?
A) 2.5 cm
B) 10 cm
C) 25 cm
D) 15 cm
Answer: B) 10 cm
6. Which of the following is not a part of a circle?
A) Radius
B) Chord
C) Diagonal
D) Arc
Answer: C) Diagonal
Explanation: "Diagonal" is a term used in polygons, not circles.
7. What do we call the boundary of a circle?
A) Diameter
B) Circumference
C) Segment
D) Sector
Answer: B) Circumference
8. Which of the following passes through the center and touches the boundary at two points?
A) Chord
B) Radius
C) Diameter
D) Arc
Answer: C) Diameter
9. If a point lies exactly at the center of the circle, its distance from any point on the circle is called —
A) Chord
B) Radius
C) Diameter
D) Arc
Answer: B) Radius
10. Two circles are called concentric if —
A) They have the same radius
B) They touch each other externally
C) They share the same center
D) They are of different colors
Answer: C) They share the same center
11. Which tool is used to draw a perfect circle in geometry?
A) Ruler
B) Divider
C) Compass
D) Protractor
Answer: C) Compass
12. Which part of a circle is greater than a semicircle but less than a full circle?
A) Minor arc
B) Major arc
C) Diameter
D) Radius
Answer: B) Major arc
13. A sector is a part of a circle enclosed by two —
A) Radii and a chord
B) Chords and an arc
C) Radii and an arc
D) Diameters
Answer: C) Radii and an arc
14. What type of triangle is formed by joining two radii and an arc of a circle?
A) Isosceles
B) Scalene
C) Right-angled
D) Equilateral
Answer: A) Isosceles
Explanation: The two radii are equal, forming two equal sides.
15. Which of the following correctly represents a semicircle?
A) Arc covering 180°
B) Chord joining two opposite points on the circle
C) Half of a full circle
D) All of the above
Answer: D) All of the above
Advanced Practice Questions – Chapter 14 Circles (With Detailed Solutions)
1. A circle has a diameter of 12 cm. A chord is drawn 4 cm away from the center. Find the length of the chord. Answer: Approximately 8.94 cm Using Pythagoras theorem: Half chord = √(r² - d²) = √(6² - 4²) = √20 ≈ 4.47. Full chord = 2 × 4.47 = 8.94 cm.
2. How many diameters can be drawn in a circle with 5 fixed points on its boundary, no three of which are collinear?
To form a diameter, we must select two opposite points. For 5 points, no pair is guaranteed to lie exactly opposite unless specified, and not all combinations form diameters.
In general, maximum number of diameters = number of distinct pairs of opposite points.
In a circle with n points, maximum diameters = n/2, only if the points are symmetrically placed.
Here, no fixed symmetry, so only 0 diameters can be guaranteed.
Answer: 0 (unless symmetry is specified)
3. If the radius of a circle is doubled, by what factor does the circumference increase?
Original circumference = 2πr
New radius = 2r → New circumference = 2π × 2r = 4πr
Factor of increase = 4πr / 2πr = 2
Answer: 2 times 4. A sector of a circle has a radius of 7 cm and an angle of 90°. Find the length of the arc. Arc length = (θ / 360°) × 2πr = (90 / 360) × 2π × 7
= (1/4) × 2 × (22/7) × 7 = (1/4) × 44 = 11 cm
Answer: 11 cm
5. A circle has a radius of 10 cm. Two chords AB = 12 cm and CD = 16 cm. Which is closer to the center?
For AB: Half of chord = 6 cm
d1 = √(102 – 62) = √(100 – 36) = √64 = 8 cm
For CD: Half of chord = 8 cm
d2 = √(100 – 64) = √36 = 6 cm
Answer: Chord CD is closer to the center
6. In how many ways can you draw a radius in a circle?
A radius can be drawn to any point on the circle’s boundary.
Answer: Infinitely many ways
7. From a point outside a circle, two tangents are drawn. Prove they are equal in length.
Tangents PA and PB from point P to circle center O.
∆OAP ≅ ∆OBP (radii equal, ∠OAP = ∠OBP = 90°, OP common)
Hence, PA = PB
Answer: Yes, tangents are equal due to congruent triangles
8. If two circles have the same center and different radii, what are they called?
Answer: Concentric Circles
Circles with the same center but different radii.
9. A chord of a circle is equal to the radius. Find the angle subtended by the chord at the center.
Triangle OAB is equilateral (OA = OB = AB = r)
Use cosine rule:
cos(θ) = (r2 + r2 – r2) / (2 × r × r) = r2 / 2r2 = 1/2
⇒ θ = 60°
Answer: 60°
10. Can two radii form a straight line? Under what condition?
Yes, when the angle between them is 180°, they form a diameter.
Answer: Yes, when both radii lie along the same line and are opposite
Answer: 0 (unless symmetry is specified)
No symmetrical points are guaranteed to lie opposite, so no diameters can be confirmed.
Why Use RD Sharma Solutions for Chapter 14?
RD Sharma solutions are very useful study material for all class 6 students as they build the foundation and helps in clearing the concepts easily.
- Clear, step-by-step explanations aligned with textbook problems
- Helps in quick revision before exams
- Boosts confidence and accuracy in solving geometry questions
- Encourages independent learning and self-assessment
- Makes the transition to higher-level geometry smoother
RD Sharma Solutions for Class 6 Maths Chapter 14 Circles FAQs
What are the key topics covered in RD Sharma Class 6 Chapter 14 Circles?
Chapter 14 of RD Sharma Class 6 focuses on fundamental concepts of circles such as radius, diameter, chord, arc, sector, and segment. It also introduces terms like concentric circles and helps students understand how to draw and identify different parts of a circle.
How do RD Sharma solutions help in understanding Class 6 Circles chapter better?
RD Sharma solutions offer step-by-step answers to textbook questions, making it easier for students to understand the logic behind each concept. The detailed explanations and visual understanding of circle-related problems enhance clarity and boost exam confidence.
Are RD Sharma Class 6 Circles solutions helpful for CBSE exams?
Yes, the solutions follow the CBSE syllabus and provide practice on all types of questions that can appear in exams. The explanations are designed to strengthen conceptual knowledge, making it ideal for Class 6 CBSE exam preparation.
Where can I download RD Sharma Class 6 Maths Solutions PDF for free?
You can find free RD Sharma Class 6 Maths Solutions PDFs on various educational platforms and websites like Infinity Learn that offer NCERT-based content.
Do RD Sharma Class 6 Maths Solutions PDFs include all chapters?
Most complete PDF solutions cover all chapters of the RD Sharma Class 6 Maths book, including important topics like Fractions, Decimals, Geometry, and Mensuration, along with Chapter 14 Circles.