Parts of a Circle Explained with Definitions and Diagram

The concept of Parts of Circle plays a key role in mathematics and is widely applicable to both real-life situations and exam scenarios. Understanding each part of a circle is essential for students of Class 6–9, as it forms the foundation for higher geometry and practical maths questions.

What Is Parts of Circle?

A circle is a two-dimensional closed figure made up of a set of points that are all equidistant from a fixed central point called the center. The concept of parts of circle includes important segments like the center, radius, diameter, chord, arc, sector, segment, and circumference. You’ll find these terms in geometry, mensuration, and everyday objects like clocks and coins.

List of Parts of Circle with Definitions

1. Centre: The fixed point from which every point on the circle is equidistant. Usually represented as ‘O’.
2. Radius: A line segment joining the centre to any point on the circle.
3. Diameter: The longest chord passing through the centre, joining two points on the circle.
4. Circumference: The distance around the circle – its curved boundary or perimeter.
5. Chord: Any line segment connecting two points on the circle, not necessarily passing through the centre.
6. Arc: A part of the circle’s circumference, forming a curved section.
7. Sector: The region enclosed by two radii and the arc between them (like a pizza slice).
8. Segment: Area enclosed between a chord and the arc, but not including the centre.
9. Tangent: A line touching the circle at exactly one point.
10. Secant: A line cutting the circle at two distinct points.

Common Differences Between Parts of a Circle

Term 1	Term 2	Difference
Radius	Diameter	Diameter = 2 × Radius. The diameter passes through the center, while the radius connects center to boundary.
Chord	Diameter	Both touch two points on the boundary, but only diameter passes through the center & is the longest chord.
Chord	Arc	Chord is straight (line segment). Arc is curved (a section of the circumference).
Segment	Sector	Segment is area between a chord and arc. Sector is area between two radii and the arc they form.
Tangent	Secant	Tangent touches at only one point; secant cuts across the circle at two points.

Real-Life Examples of Parts of Circle

Parts of circle appear everywhere!

• A clock face—radius is hour hand, circumference is the rim, centre is center of clock.
• Bicycle or car wheel—spokes are radii, rim is circumference, patches of tyre represent arcs and chords.
• Pizza slices—each is a sector. The crust can be seen as the arc of a sector.
• Coins—edges = circumference, line from centre to edge = radius.

Recognizing such parts around you makes learning circle geometry memorable and practical!

Key Formulas for Parts of Circle

Here are the most important formulas:

• Circumference: \( C = 2\pi r \) or \( C = \pi d \)
• Diameter: \( d = 2r \)
• Area: \( A = \pi r^2 \)
• Length of arc (for angle θ in degrees): \( L = \frac{\theta}{360^{\circ}} \times 2\pi r \)
• Area of sector: \( \frac{\theta}{360^{\circ}} \times \pi r^2 \)

Step-by-Step Example: Identify and Calculate

Question: The circumference of a wheel is 154 cm. Find its radius.

1. Formula for circumference: \( C = 2\pi r \ )

2. Substitute values: \( 154 = 2 \times \frac{22}{7} \times r \)

3. Rearranging: \( r = \frac{154 \times 7}{2 \times 22} \)

4. Calculate: \( r = \frac{1078}{44} = 24.5 \) cm

5. Final Answer: The radius is 24.5 cm

Try These Yourself

• Label the eight parts of circle on a drawn diagram.
• Find the length of an arc if the radius is 7 cm and angle made is 60°.
• What is the difference between a segment and a sector?
• Which is longer: a chord or a radius? Why?

Frequent Errors and Misunderstandings

• Mixing up ‘diameter’ and ‘chord’.
• Thinking the center is on the circumference (it is not).
• Assuming all arcs are semicircles—arcs can be any length.
• Forgetting diameter is always 2× radius.
• Writing area or circumference in wrong units.

Relation to Other Concepts

The idea of parts of circle connects directly to area of a circle and perimeter/circumference problems. Mastering these terms also helps in understanding circle theorems and coordinate geometry later in your studies.

Classroom Tip

A quick way to remember the parts of circle is to use different colors for each segment in your diagrams. Mnemonics like “RDC-ACTS” (Radius, Diameter, Circumference, Arc, Chord, Tangent, Sector) help students recall all key terms. Vedantu’s teachers often use simple real-world objects to reinforce these ideas in their live sessions.

We explored Parts of Circle—from definition, formula, examples, mistakes, and connections to other subjects. Continue practicing with Vedantu to become confident in geometry and score well in all maths exams.

Explore more: Area of a Circle | Circumference of a Circle | Chord, Arc, Tangent of a Circle | Segments and Sectors of a Circle