---
title: "NCERT Solutions for Class 9 Maths Chapter 5 Exercise 5.1"
url: https://www.swavid.com/maths/class/9/chapter/i-m-up-and-down-and-round-and-round/ncert-solutions/exercise-5-1
dateModified: 2026-10-07T15:44:30+00:00
---

# NCERT Solutions for Class 9 Maths Chapter 5 Exercise 5.1

Chapter 5: I’m Up and Down, and Round and Round. Every question from Exercise 5.1, with full working and the final answer.

Free PDF (26 pages): https://www.swavid.com/api/seo/pdf/ncert/maths/class-9/swavid-ncert-solutions-class-9-maths-chapter-5-i-m-up-and-down-and-round-and-round-3f5dbc3f8b.pdf

## Exercise Set 5.1

### Question 1

*3 marks · Short answer*

Draw $\Delta ABC$ with $AB = 5\text{ cm}$, $\angle A = 70^\circ$ and $\angle B = 60^\circ$. Draw the circumcircle of $\Delta ABC$. Is the centre inside or outside the triangle?

**Solution**

1. Construct triangle $ABC$ with $AB = 5\text{ cm}$, $\angle A = 70^\circ$ and $\angle B = 60^\circ$.
2. Draw perpendicular bisectors of any two sides, say $AB$ and $BC$, to intersect at point $O$.
3. The circumcentre $O$ lies inside the triangle since $\Delta ABC$ is an acute-angled triangle.

**Answer:** The centre is inside the triangle.

> Common mistake: Drawing the bisectors of the angles instead of perpendicular bisectors of the sides.

### Question 2

*3 marks · Short answer*

Draw $\Delta ABC$ with $AB = 5\text{ cm}$, $\angle A = 100^\circ$, $AC = 4\text{ cm}$. Draw the circumcircle of $\Delta ABC$. Is the centre inside or outside the triangle?

**Solution**

1. Construct triangle $ABC$ with $AB = 5\text{ cm}$, $\angle A = 100^\circ$ and $AC = 4\text{ cm}$.
2. Draw perpendicular bisectors of sides $AB$ and $AC$ to intersect at point $O$.
3. The circumcentre $O$ lies outside the triangle since $\Delta ABC$ is an obtuse-angled triangle.

**Answer:** The centre is outside the triangle.

> Common mistake: Confusing acute and obtuse triangle circumcentre locations.

### Question 3

*3 marks · Short answer*

Draw $\Delta ABC$, with $AB = 6\text{ cm}$, $BC = 7\text{ cm}$ and $CA = 7\text{ cm}$. Draw the circumcircle of $\Delta ABC$. Let the circumcentre be $O$. Measure $OA$, $OB$, $OC$.

**Solution**

1. Construct triangle $ABC$ with sides $AB = 6\text{ cm}$, $BC = 7\text{ cm}$ and $CA = 7\text{ cm}$.
2. Draw the perpendicular bisectors of the sides to locate the circumcentre $O$.
3. Measure the distances from $O$ to the vertices, obtaining $OA = OB = OC$ (approximately $3.9\text{ cm}$).

**Answer:** $OA = OB = OC \approx 3.9\text{ cm}$

> Common mistake: Inaccurate construction leading to unequal distances from the centre to the vertices.

### Question 4

*2 marks · Very short answer*

What is the least possible radius of a circle through two points A and B?

**Solution**

1. The smallest circle passing through two points $A$ and $B$ has the line segment $AB$ as its diameter.
2. The radius of this circle is half the length of $AB$.

**Answer:** Half the distance between A and B.

> Common mistake: Stating the radius equals the full length of AB instead of half.

## Related pages

- [All Chapter 5 NCERT solutions](https://www.swavid.com/maths/class/9/chapter/i-m-up-and-down-and-round-and-round/ncert-solutions)
- [Exercise 5.2](https://www.swavid.com/maths/class/9/chapter/i-m-up-and-down-and-round-and-round/ncert-solutions/exercise-5-2)
- [Exercise 5.3](https://www.swavid.com/maths/class/9/chapter/i-m-up-and-down-and-round-and-round/ncert-solutions/exercise-5-3)
- [Exercise 5.4](https://www.swavid.com/maths/class/9/chapter/i-m-up-and-down-and-round-and-round/ncert-solutions/exercise-5-4)
- [Exercise 5.5](https://www.swavid.com/maths/class/9/chapter/i-m-up-and-down-and-round-and-round/ncert-solutions/exercise-5-5)
- [Exercise 5.6](https://www.swavid.com/maths/class/9/chapter/i-m-up-and-down-and-round-and-round/ncert-solutions/exercise-5-6)

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