---
title: "NCERT Solutions for Class 9 Maths Chapter 5 Exercise 5.2"
url: https://www.swavid.com/maths/class/9/chapter/i-m-up-and-down-and-round-and-round/ncert-solutions/exercise-5-2
dateModified: 2026-10-07T15:44:30+00:00
---

# NCERT Solutions for Class 9 Maths Chapter 5 Exercise 5.2

Chapter 5: I’m Up and Down, and Round and Round. Every question from Exercise 5.2, 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 5.2

### Question 1

*3 marks · Proof*

Show that the triangle formed by a chord and the centre of the circle is isosceles.

**Solution**

1. Let AB be a chord of a circle with centre C.
2. Join CA and CB to form ∃CAB.
3. Since CA and CB are both radii of the same circle, $CA = CB$.
4. Therefore, ∃CAB is an isosceles triangle.
5. Hence proved.

**Answer:** Hence proved that the triangle formed by a chord and the centre is isosceles.

> Common mistake: Forgetting to state that the two sides are radii of the same circle.

### Question 2

*4 marks · Proof*

Show that if two such isosceles triangles (occurring in the previous question) have equal base length, they are congruent to each other.

**Solution**

1. Let $\Delta CAB$ and $\Delta C'A'B'$ be two triangles formed by chords $AB$ and $A'B'$ with their respective centres $C$ and $C'$.
2. We are given that the base lengths are equal, so $AB = A'B'$.
3. The other two sides of each triangle are radii of the circles, so $CA = CB = C'A' = C'B'$.
4. By SSS congruence, $\Delta CAB \cong \Delta C'A'B'$.
5. Hence proved.

**Answer:** Hence proved that the two isosceles triangles are congruent to each other.

> Common mistake: Assuming the circles have the same radius without justification if not specified, though base equality and radii properties apply.

## 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 5.1](https://www.swavid.com/maths/class/9/chapter/i-m-up-and-down-and-round-and-round/ncert-solutions/exercise-5-1)
- [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