Class 10 Maths Chapter 10 Circles carries about 3 to 4 marks in the CBSE Board exam and builds on the basic circle ideas from earlier classes. These notes cover the tangent to a circle, the number of tangents from a point, and the two key tangent theorems in a hand-drawn revision style.
- CBSE Board: about 3 to 4 marks, usually one tangent-property proof plus one short tangent-length sum
- JEE Main: rarely a direct question, but the tangent and radius rule supports coordinate-geometry circle problems
These notes are prepared by Collegedunia subject mentors, matched to the 2026-27 NCERT print and recent CBSE Board papers.
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Table of Contents |
Watch Circles Class 10 Maths Chapter 10 Tangents Explained
Source: Magnet Brains on YouTube
Circles Handwritten Notes: Complete Diagram Inventory for Class 10 Maths
These notes hold 6 hand-sketched diagrams you can copy onto rough paper. The table maps each figure to its page.
| Page | Diagram | What It Shows |
|---|---|---|
| 2 | Secant versus tangent sketch | A line cutting the circle at two points beside a line touching it at exactly one point |
| 3 | Tangent and radius diagram | The radius drawn to the point of contact, meeting the tangent at a right angle |
| 4 | Tangents from a point | Three cases side by side: a point inside (0), on (1), and outside (2) the circle |
| 5 | Two-tangents diagram | Two tangents from one external point with the equal segments and symmetric kite marked |
| 6 | Proof flow for equal tangents | The arrow chain using congruent right triangles that shows the two tangent lengths are equal |
| 7 | Last-day mind map | One-page tree linking the tangent definition to both theorems and the tangent-count cases |
Topics Covered in Class 10 Maths Chapter 10 Circles Handwritten Notes
The notebook opens with the tangent to a circle, the line that meets it at one point, against a secant that cuts at two. The first theorem: the tangent is perpendicular to the radius at the point of contact. The notes then count tangents from a point: 0 inside, 1 on, and 2 outside. The second theorem proves the two tangents from an external point are equal.
Circles Handwritten Notes: Memory Mnemonics for the Tangent Rules
Three mnemonics the notebook leans on.
How will Collegedunia's Handwritten Notes Help You with Circles?
These notes turn a proof-heavy chapter into a 9-page revision stack.
- Hand-Sketched Visual Anchors: The tangent-and-radius diagram, two-tangents diagram, and proof flow are drawn freehand.
- Colour-Coded Box Legend: Orange for definitions, blue for theorems, yellow for exam traps, red for common errors.
- 2026-27 NCERT Alignment: Every page matches the current print, so you revise only the tangent content the latest syllabus tests.
- Proof-First Layout: The two theorems are numbered steps, the exact form CBSE wants.
Circles Handwritten Notes: Color Legend for the Notebook
These notes use four ink colours in a fixed way, so you can skim all 9 pages in minutes.
| Colour | Box Type | What's Inside |
|---|---|---|
| Orange | Definition box | NCERT one-line definitions: tangent, point of contact, secant, external point |
| Blue | Theorem box | The tangent-radius perpendicularity rule and the equal-tangents result, each with a labelled sketch |
| Yellow | Exam-trap callout | Common traps, like confusing a tangent with a secant or miscounting tangents from a point |
| Red | Common-mistake box | Wrong proof steps shown next to the correct numbered form |
Circles Key Results for Class 10 Maths Quick Recall
These results cover nearly every tangent numerical CBSE asks. The full working sits on the Formula Sheet.
| Idea | Relation |
|---|---|
| Tangent and radius rule | The radius to the point of contact is perpendicular to the tangent, so the angle is 90∘ |
| Tangent length by Pythagoras | For a circle of radius r and external point at distance d from the centre, tangent length = √d2 - r2 |
| Number of tangents from a point | 0 if inside, 1 if on, and 2 if outside the circle |
| Equal tangents | The two tangents from one external point have equal length, PA = PB |
Full formula table: Circles Class 10 Maths Formula Sheet
Circles: Last 24-Hour Revision Card for Class 10 Maths
Scan the page below the night before the Board exam.
- Tangent definition: a line meeting the circle at exactly one point, the point of contact. A secant cuts at two points.
- Tangent and radius: the tangent at any point is perpendicular to the radius through the point of contact. This 90 degree angle drives the sums.
- Number of tangents: 0 from a point inside, 1 from a point on, and 2 from a point outside the circle.
- Equal tangents: the two tangents from an external point are equal. A favourite short-answer proof.
- Tangent length: tangent length is √d2 - r2, with d the distance to the centre and r the radius.
Circles Class 10 Maths Self-Assessment Quick Quiz
Four MCQs in the style CBSE asks. Tap each question to reveal the answer.
Q1. A line that meets a circle at exactly one point is called a:
(a) secant (b) chord (c) tangent (d) diameter
Answer: (c) tangent, since a tangent touches the circle at a single point of contact.
Q2. How many tangents can be drawn from a point outside a circle?
(a) 0 (b) 1 (c) 2 (d) infinite
Answer: (c) 2, because exactly two tangents can be drawn from a point lying outside the circle.
Q3. The radius of a circle is 5 cm and a point is 13 cm from the centre. The tangent length is:
(a) 8 cm (b) 12 cm (c) 18 cm (d) 169 cm
Answer: (b) 12 cm, since the tangent length is √132 - 52 = √144 = 12 cm.
Q4. The angle between a tangent and the radius at the point of contact is:
(a) 45 degrees (b) 60 degrees (c) 90 degrees (d) 180 degrees
Answer: (c) 90 degrees, because the tangent is perpendicular to the radius through the point of contact.
Student Feedback
71% of Class 10 students told us they revise Circles fastest from hand-drawn pages, and 4 out of 5 said the freehand tangent-and-radius sketch made the right-angle rule finally stick the night before the board exam. The most-redrawn sketch was the two-tangents diagram for the equal-tangent proof.
Students who copied the colour-coded boxes onto rough paper reported finishing the whole chapter recall in under 25 minutes, and the 24-hour revision card was rated the single most useful page by 64% of the poll.
Source: 2026-27 Class 10 Maths student poll, 8,600 students from CBSE schools in 14 states, before the 2026 boards.
Other Resources for This Chapter
Pair these handwritten notes with the other Class 10 Maths resources for this chapter, all linked below.
| Resource | Open |
|---|---|
| NCERT Solutions | Circles Class 10 Maths NCERT Solutions |
| Notes | Circles Class 10 Maths Notes |
| Formula Sheet | Circles Class 10 Maths Formula Sheet |
| NCERT Book PDF | Circles Class 10 Maths NCERT Book PDF |
| NCERT Exemplar Solutions | Circles Class 10 Maths NCERT Exemplar Solutions |
| NCERT Exemplar Solutions | Circles Class 10 Maths NCERT Exemplar PDF |
| Handwritten Notes | Circles Class 10 Maths Handwritten Notes |
NCERT Handwritten Notes for Class 10 Maths: All Chapters
Jump to another Class 10 Maths chapter's notes below.
| Chapter | Resource |
|---|---|
| Chapter 8 | Introduction to Trigonometry Handwritten Notes |
| Chapter 9 | Some Applications of Trigonometry Handwritten Notes |
| Chapter 11 | Areas Related to Circles Handwritten Notes |
| Chapter 12 | Surface Areas and Volumes Handwritten Notes |
Circles Class 10 Maths Handwritten Notes FAQs
Ques. Where can I download Circles Class 10 Maths Handwritten Notes PDF?
Ans. You can download the Circles Class 10 Maths Handwritten Notes PDF directly from this page. The notes are free and ready to print.
Ques. Are these handwritten notes aligned with the 2026-27 NCERT?
Ans. Yes. The notebook follows the current 2026-27 syllabus for Class 10 Maths. It centres on the tangent to a circle, the number of tangents from a point, and the two tangent theorems.
Ques. What is a tangent to a circle?
Ans. A tangent to a circle is a line that meets the circle at exactly one point, called the point of contact. It differs from a secant, which cuts the circle at two points. The sketch on page 2 shows this difference.
Ques. How many tangents can be drawn to a circle from an external point?
Ans. Exactly two tangents can be drawn from a point outside the circle. A point on the circle gives one, and a point inside gives none. The diagram on page 4 lays out all three cases.
Ques. What is the relation between a tangent and the radius at the point of contact?
Ans. The tangent at any point of a circle is perpendicular to the radius drawn to the point of contact, so the angle between them is 90 degrees. The blue theorem box on page 3 carries a labelled solved example using this rule.
Ques. How do the notes prove that two tangents from an external point are equal?
Ans. The proof on page 6 uses congruent right triangles. You join the centre to the external point and to both points of contact, then show the two right triangles are congruent. So the tangent lengths are equal, written PA = PB.
Ques. What's the difference between Collegedunia's Handwritten Notes and the regular Notes for this chapter?
Ans. The regular Notes give the full concept walkthrough with detailed text. The Handwritten Notes compress the same content into a faster, more visual tool with hand-drawn diagrams, colour-coded boxes, and a 24-hour recall card. Use Notes for the first read and Handwritten Notes for quick revision.
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