NCERT Solutions for Class 10 Mathematics Chapter Circles

This worksheet provides complete and accurate NCERT Solutions for Class 10 Mathematics Chapter Circles. The chapter focuses on important concepts related to circles, especially tangents and their properties. It helps students understand how lines interact with circles and how geometric reasoning is applied. This worksheet is useful for strengthening conceptual clarity and preparing for school exams, as all solutions strictly follow NCERT standards.

Chapter summary: stories, poems & themes

This chapter is concept-based and does not include stories or poems. It focuses on geometric understanding through diagrams, activities, and theorems. Students learn about the position of a line with respect to a circle, including secant, tangent, and non-intersecting lines. The chapter also includes activity-based learning where students observe how tangents behave and how many tangents can be drawn from different positions relative to a circle.

What this NCERT chapter covers?

• Understanding tangent, secant, and non-intersecting lines 
• Properties of tangents to a circle 
• Relationship between radius and tangent 
• Number of tangents from a point inside, on, or outside a circle 
• Equal lengths of tangents from an external point 
• Application of theorems in problem solving 

How to use these NCERT solutions?

Students should first attempt all questions from the worksheet on their own. After solving, they can use these NCERT Solutions to check their answers and understand correct methods. Parents and teachers can guide students using these solutions, ensuring that the approach matches NCERT standards. Since all answers follow the exact NCERT order, it becomes easier for revision and exam preparation.

Student tips & learning tricks

Focus on understanding the concept of tangents rather than memorizing. Remember that the radius is always perpendicular to the tangent at the point of contact. Practice diagram-based questions carefully, as mistakes often happen in interpretation. While solving problems, clearly identify given values and apply the correct theorem step-by-step.

Why NCERT solutions are important?

NCERT Solutions help students build a strong foundation in mathematics. They ensure that concepts are understood correctly as per the CBSE curriculum. These solutions improve accuracy, boost confidence, and help students perform better in exams. Regular practice with NCERT-aligned solutions makes problem-solving easier and more systematic.

Complete answer key – NCERT solutions

Exercise 10.1

1. 
1 

2. 
(i) 1 
(ii) secant 
(iii) 2 
(iv) point of contact 

3. 
1 – b 

4. 
student-generated activity 

Exercise 10.2

1. 
1 – a 

2. 
2 – b 

3. 
3 – a 

4. 
Given: Diameter AB, tangents at A and B 
OA ⟂ tangent at A 
OB ⟂ tangent at B 
Both tangents are perpendicular to the same line 
Hence, tangents are parallel 

5. 
Radius is perpendicular to tangent at point of contact 
Hence, perpendicular passes through centre 

6. 
Radius = 3 cm 

7. 
Chord length = 8 cm 

8. 
AB + CD = AD + BC 

9. 
∠ AOB = 90° 

10. 
Angle between tangents + angle at centre = 180° 

11. 
Parallelogram becomes rhombus as all sides are equal 

12. 
AB = 14 cm 
AC = 12 cm 

13. 
Opposite sides subtend supplementary angles at the centre 

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