Circles (Grade 5)
A circle is a closed curve where every point on the curve is at the same distance from a fixed point called the centre. Circles are everywhere — wheels, coins, bangles, clocks, and plates.
The circle is a unique shape. It has no corners, no edges, and infinite lines of symmetry. It is the only shape where every point on the boundary is equally distant from the centre.
In Class 5, you will learn the important terms related to circles — radius, diameter, chord, arc, and circumference — and understand how they relate to each other. You will also practise drawing circles with a compass.
What is Circles - Class 5 Maths (Geometry)?
A circle is a set of all points in a plane that are at a fixed distance from a fixed point.
- Centre (O): The fixed point inside the circle.
- Radius (r): The distance from the centre to any point on the circle.
- Diameter (d): A line segment passing through the centre with both endpoints on the circle. Diameter = 2 × Radius.
- Chord: A line segment with both endpoints on the circle. The diameter is the longest chord.
- Arc: A part (curve) of the circle between two points on it.
- Circumference: The total distance around the circle (its perimeter).
- Semicircle: Half of a circle, formed by a diameter.
Circles (Grade 5) Formula
Diameter = 2 × Radius | Radius = Diameter ÷ 2
Types and Properties
Important Parts of a Circle:
| Term | Definition | Key Fact |
|---|---|---|
| Centre | Fixed point inside the circle | Not on the circle itself |
| Radius | Centre to any point on circle | All radii are equal |
| Diameter | Passes through centre, both ends on circle | Longest chord, = 2r |
| Chord | Both endpoints on circle | May or may not pass through centre |
| Arc | A curved part of the circle | Minor arc (smaller), major arc (larger) |
| Circumference | Distance around the circle | Like the perimeter of a circle |
Drawing a circle: Use a compass. Fix the pointed end at the centre, set the pencil end at the required radius, and rotate fully to draw the circle.
Solved Examples
Example 1: Example 1: Finding Diameter from Radius
Problem: The radius of a circle is 7 cm. Find the diameter.
Solution:
Step 1: Diameter = 2 × Radius
Step 2: Diameter = 2 × 7 = 14 cm
Answer: The diameter is 14 cm.
Example 2: Example 2: Finding Radius from Diameter
Problem: A circular plate has a diameter of 30 cm. What is its radius?
Solution:
Step 1: Radius = Diameter ÷ 2
Step 2: Radius = 30 ÷ 2 = 15 cm
Answer: The radius is 15 cm.
Example 3: Example 3: Identifying Parts
Problem: In a circle with centre O, AB is a line segment passing through O with A and B on the circle. What is AB called?
Solution:
Step 1: AB has both endpoints on the circle → it is a chord.
Step 2: AB passes through the centre O → it is a special chord called the diameter.
Answer: AB is a diameter.
Example 4: Example 4: Chord vs Diameter
Problem: PQ is a chord of a circle but does not pass through the centre. Is PQ a diameter?
Solution:
Step 1: A diameter must pass through the centre.
Step 2: PQ does not pass through the centre.
Answer: No, PQ is a chord but not a diameter.
Example 5: Example 5: Radius of a Wheel
Problem: Aman's bicycle wheel has a diameter of 60 cm. What is the radius?
Solution:
Step 1: Radius = Diameter ÷ 2 = 60 ÷ 2 = 30 cm.
Answer: The radius is 30 cm.
Example 6: Example 6: Drawing a Circle
Problem: Draw a circle of radius 4 cm using a compass.
Solution:
Step 1: Open the compass to 4 cm using a ruler.
Step 2: Fix the pointed end on the paper. This is the centre.
Step 3: Keeping the pointed end fixed, rotate the pencil end fully around.
Step 4: Mark the centre as O.
Answer: A circle with radius 4 cm is drawn.
Example 7: Example 7: True or False
Problem: "The diameter is always the longest chord of a circle." True or False?
Solution:
Step 1: A chord is any line segment with endpoints on the circle.
Step 2: The diameter passes through the centre, making it the farthest-spanning chord.
Step 3: Any other chord does not pass through the centre, so it is shorter.
Answer: True.
Example 8: Example 8: Concentric Circles
Problem: Two circles have the same centre but radii of 3 cm and 5 cm. What are they called?
Solution:
Step 1: Circles with the same centre but different radii are called concentric circles.
Answer: They are concentric circles.
Example 9: Example 9: Number of Diameters
Problem: How many diameters can a circle have?
Solution:
Step 1: A diameter is any chord passing through the centre.
Step 2: You can draw a line through the centre in any direction, and it will be a diameter.
Answer: A circle has infinitely many diameters. All of them have the same length.
Example 10: Example 10: Real-Life Circle
Problem: Aditi's bangle has a radius of 3.5 cm. What is the diameter?
Solution:
Step 1: Diameter = 2 × 3.5 = 7 cm.
Answer: The diameter of the bangle is 7 cm.
Real-World Applications
Where do we see circles?
- Wheels: All wheels are circular. The axle is at the centre. Because every point on the circle is the same distance from the centre, the ride is smooth.
- Coins: Most coins (₹1, ₹2, ₹5, ₹10) are circular in shape.
- Clocks: Clock faces are circles with the centre at the pivot of the hands. The numbers are evenly spaced on the circumference.
- Sports: Cricket ground centre circle, basketball hoops, shot put rings, and discus throwing circles.
- Kitchen: Plates, rotis, chapatis, dosa, idlis, and lids of vessels are circular.
- Bangles and rings: Worn on wrists and fingers — perfect circles.
- Dartboards and targets: Concentric circles are used in archery targets and dartboards.
- Ferris wheels and merry-go-rounds: Move in circular paths.
Key Points to Remember
- A circle is a closed curve with all points at the same distance from the centre.
- Radius = distance from centre to the circle. All radii are equal.
- Diameter = 2 × Radius. It is the longest chord.
- A chord connects two points on the circle. A diameter is a chord that passes through the centre.
- An arc is a part of the circle’s curve.
- The circumference is the distance around the circle.
- A circle has infinitely many radii, diameters, and chords.
- Circles with the same centre but different radii are concentric circles.
Practice Problems
- The radius of a circle is 9 cm. Find its diameter.
- The diameter of a circular coin is 2.5 cm. Find its radius.
- Draw two concentric circles with radii 3 cm and 5 cm.
- Name the longest chord of a circle.
- A chord PQ of a circle passes through the centre. What is PQ called?
- Can a chord be longer than the diameter? Explain.
- Dev draws a circle with diameter 16 cm. What compass opening (radius) did he use?
- How many radii can a circle have?
Frequently Asked Questions
Q1. What is a circle?
A circle is a closed curve where every point is at the same distance from a fixed point called the centre. It has no corners or edges.
Q2. What is the relationship between radius and diameter?
The diameter is twice the radius. Diameter = 2 × Radius, and Radius = Diameter ÷ 2.
Q3. What is a chord?
A chord is a straight line segment with both endpoints on the circle. The diameter is the longest possible chord, as it passes through the centre.
Q4. How many diameters does a circle have?
A circle has infinitely many diameters. You can draw a diameter in any direction through the centre. All diameters of a given circle have the same length.
Q5. What is the difference between a radius and a diameter?
A radius goes from the centre to the circle (half-way across). A diameter goes from one side of the circle to the other, passing through the centre (all the way across). The diameter is twice the radius.
Q6. What are concentric circles?
Concentric circles are two or more circles that share the same centre but have different radii. For example, a dartboard has concentric circles.
Q7. What is circumference?
Circumference is the total distance around the circle, like the perimeter of a polygon. You will learn the formula for circumference (using pi) in higher classes.
Q8. Is the centre of a circle on the circle?
No. The centre is a point inside the circle. It is at an equal distance (the radius) from every point on the circle.
Q9. What tool is used to draw a circle?
A compass is used to draw a circle. Set the compass to the required radius and rotate it around the fixed point (centre).
Q10. Is this topic in the NCERT Class 5 syllabus?
Yes. Circles, their parts (radius, diameter, chord), and drawing circles with a compass are part of the Geometry chapter in NCERT/CBSE Class 5 Maths.
Related Topics
- Quadrilaterals (Grade 5)
- Circles (Grade 4)
- Lines, Line Segments and Rays
- Parallel and Perpendicular Lines
- Angles (Grade 5)
- Angle Sum Property of Triangle
- Types of Triangles (Grade 5)
- Symmetry (Grade 5)
- Reflection and Rotation
- Nets of 3D Shapes (Grade 5)
- Views of 3D Shapes (Grade 5)
- Complementary and Supplementary Angles
