---
title: "NCERT Solutions for Class 10 Maths Chapter 10 Exercise 10.1"
url: https://www.swavid.com/maths/class/10/chapter/circles/ncert-solutions/exercise-10-1
dateModified: 2026-10-07T15:54:33+00:00
---

# NCERT Solutions for Class 10 Maths Chapter 10 Exercise 10.1

Chapter 10: Circles. Every question from Exercise 10.1, with full working and the final answer.

Free PDF (9 pages): https://www.swavid.com/api/seo/pdf/ncert/maths/class-10/swavid-ncert-solutions-class-10-maths-chapter-10-circles-1a2f8617f9.pdf

## EXERCISE 10.1

### Question 1

*2 marks · Very short answer*

How many tangents can a circle have?

**Solution**

1. A circle is made up of infinitely many points.
2. Since there is one tangent at each point on the circle, a circle can have infinitely many tangents.

**Answer:** Infinitely many

> Common mistake: Writing finite numbers like two or four.

### Question 2

*1 mark · Fill in the blank*

Fill in the blanks :
(i) A tangent to a circle intersects it in _______ point (s).
(ii) A line intersecting a circle in two points is called a _______.
(iii) A circle can have _______ parallel tangents at the most.
(iv) The common point of a tangent to a circle and the circle is called _______.

**Part (i)**

1. A tangent is defined as a line that intersects the circle at only one point.

Answer (i): one

**Part (ii)**

1. A line intersecting a circle in two points is called a secant of the circle.

Answer (ii): secant

**Part (iii)**

1. A circle can have at most two parallel tangents to a given secant or parallel to each other.

Answer (iii): two

**Part (iv)**

1. The common point of a tangent to a circle and the circle is called the point of contact.

Answer (iv): point of contact

**Answer:** (i) one (ii) secant (iii) two (iv) point of contact

> Common mistake: Confusing the number of parallel tangents with the infinite number of tangents that can be drawn on a circle.

### Question 3

*1 mark · MCQ*

A tangent $PQ$ at a point $P$ of a circle of radius $5\text{ cm}$ meets a line through the centre $O$ at a point $Q$ so that $OQ = 12\text{ cm}$. Length $PQ$ is :

- $12\text{ cm}$
- $13\text{ cm}$
- $8.5\text{ cm}$
- $\sqrt{119}\text{ cm}$

**Solution**

1. Since the tangent at any point of a circle is perpendicular to the radius through the point of contact, triangle OPQ is a right-angled triangle at P.
2. Using Pythagoras theorem, $OQ^2 = OP^2 + PQ^2$, which gives $12^2 = 5^2 + PQ^2$, so $PQ = \sqrt{144 - 25} = \sqrt{119}\text{ cm}$.

**Answer:** (D) $\sqrt{119}\text{ cm}$

> Common mistake: Adding the squares instead of subtracting, leading to $13\text{ cm}$.

### Question 4

*3 marks · Short answer*

Draw a circle and two lines parallel to a given line such that one is a tangent and the other, a secant to the circle.

**Solution**

1. Draw a given line \(l\) and a circle in a plane.
2. Draw a line \(m\) parallel to \(l\) such that it intersects the circle at only one point, making it a tangent.
3. Draw another line \(n\) parallel to \(l\) such that it intersects the circle at two points, making it a secant.

**Answer:** A circle with one tangent and one secant parallel to a given line.

> Common mistake: Drawing lines that are not parallel to the given line.

## Related pages

- [All Chapter 10 NCERT solutions](https://www.swavid.com/maths/class/10/chapter/circles/ncert-solutions)
- [Exercise 10.2](https://www.swavid.com/maths/class/10/chapter/circles/ncert-solutions/exercise-10-2)

Solutions written by SwaVid, a personal AI tutor for Class 6 to 10 Maths and Science. Practise this chapter free: https://www.swavid.com/start/student