TEACHGYAN • CLASS 10 MATHEMATICS • NCERT 2026–27
Chapter 10: Circles
Detailed Notes • Worked Examples • Competency • Board Practice
📖 Chapter Explanation
The chapter studies tangent properties and the geometry of circles. Students understand why the radius to the point of contact is perpendicular to the tangent and use tangent lengths from an external point.
🧭 Concept Journey
📌 Core Concepts
The tangent at a point on a circle is perpendicular to the radius through that point. From an external point, the two tangent segments to a circle are equal.
💡 Worked Example
The tangent at a point on a circle is perpendicular to the radius through that point. From an external point, the two tangent segments to a circle are equal.
⚠️ Common Errors
If PA and PB are tangents from P, then PA=PB. This equality can simplify perimeter and length problems involving tangents.
🧠 Concept-Based MCQs
- A circular park has two tangent paths from the same entrance point. Students explain why the path lengths are equal and use the property in a calculation.
Answer Key: 1-B, 2-B, 3-B, 4-B.
📊 Case-Based / Competency
A tangent touches a circle at exactly one point. Do not confuse a tangent with a secant, which intersects the circle at two points.
- Draw or identify the mathematical model.
- Select the relevant theorem/formula.
- Solve with complete working.
- Interpret and verify the answer.
🔎 Extension Case
A tangent touches a circle at: A) no point B) one point C) two points D) three points|Radius to the point of contact is: A) parallel to tangent B) perpendicular to tangent C) equal to tangent D) a secant|Tangents from the same external point are: A) unequal B) equal C) perpendicular always D) diameters|A secant intersects a circle at: A) one point B) two points C) no points D) centre only
🔥 HOTS & Board Challenge
- Explain why the chosen method works.
- Create a similar problem and solve it.
- Find and correct a plausible incorrect solution.
- Apply the concept to a new context.
✍️ Exam Practice
- Define the central concept.
- Solve a direct application problem.
- Solve a multi-step competency problem.
- Interpret a diagram/context.
- Write a 5-mark solution with reasoning.
📄 Practice Worksheet
- 5 concept checks
- 5 standard problems
- 3 applications
- 2 case-based questions
- 2 HOTS questions
- 1 board challenge
🎯 One-Minute Revision
circle → tangent → point of contact → radius perpendicular to tangent → equal tangents
🏆 Mastery Checklist
- ☐ I understand the concept.
- ☐ I can choose the correct method.
- ☐ I can solve step by step.
- ☐ I can handle competency questions.
- ☐ I can verify and interpret my answer.
← Class 10 Mathematics Free Resources | ← Class 10 Main Page
Original explanatory study material aligned to NCERT/CBSE topics; textbook passages are not reproduced verbatim.