NCERT Class 10 Mathematics Mathematics: Chapter 10 — MATHEMATICS
This chapter, "Circles," from NCERT Class 10 Mathematics, introduces the concept of a circle and its related terms like radius, chord, and segment. It explores the relationship between a circle and a line in a plane, identifying three possibilities: a non-intersecting line, a secant intersecting at two points, and a tangent touching the circle at a single point. The chapter emphasizes that a tangent is a special case of a secant where the two intersection points of the chord coincide. It also highlights that there is only one unique tangent at any given point on a circle. This foundational understanding of tangents is crucial for further study in geometry and prepares students for CBSE examinations.
Quick info
| Board | CBSE / NCERT |
|---|---|
| Class | Class 10 |
| Subject | Mathematics |
| Book | Mathematics |
| Chapter | Chapter 10 — MATHEMATICS |
| Language | English |
| PDF type | NCERT Textbook |
| Session | CBSE 2026 |
| Reading time | 4 minutes |
| Word count | 651 |
Learning outcomes
- Define a circle and recall related terms.
- Differentiate between a non-intersecting line, a secant, and a tangent to a circle.
- Understand that a tangent intersects a circle at exactly one point.
- Recognize a tangent as a limiting case of a secant.
- Understand the uniqueness of a tangent at a point on a circle.
Vocabulary
| Word | Meaning |
|---|---|
| Circle | A collection of all points in a plane which are at a constant distance (radius) from a fixed point (centre). |
| Radius | The constant distance from the centre to any point on the circle. |
| Chord | A line segment whose endpoints lie on the circle. |
| Secant | A line that intersects a circle at two distinct points. |
| Tangent | A line that intersects a circle at exactly one point. |
| Non-intersecting line | A line that has no common point with the circle. |
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Practice questions
- What are the three possible relationships between a line and a circle in a plane? Answer: A line can be non-intersecting, a secant, or a tangent to a circle.
- How many points does a secant have in common with a circle? Answer: A secant has two points in common with a circle.
- Define a tangent to a circle. Answer: A tangent to a circle is a line that intersects the circle at only one point.
- What is the relationship between a tangent and a secant? Answer: A tangent is a special case of a secant when the two endpoints of its corresponding chord coincide.
Frequently asked questions
What is a circle?
A circle is defined as the set of all points in a plane that are equidistant from a fixed point called the centre.
What is a secant of a circle?
A secant is a line that intersects a circle at two distinct points.
What is a tangent to a circle?
A tangent is a line that touches the circle at exactly one point.
Can a line intersect a circle at more than two points?
No, a line can intersect a circle at a maximum of two points.
Is a tangent a special type of secant?
Yes, a tangent is considered a special case of a secant where the two intersection points merge into one.
How many tangents can be drawn to a circle at a single point?
Only one unique tangent can be drawn to a circle at any given point on the circle.
Related resources
Important topics
Topics covered
NCERT Class 10 Mathematics — Mathematics — Chapter 10 — MATHEMATICS. Verified by NCERT Help Editorial Team. Reviewed on 29 Jul 2026. Last updated 10 Aug 2026.