---
title: "NCERT Solutions for Class 9 Maths Chapter 5 Exercise 5.6"
url: https://www.swavid.com/maths/class/9/chapter/i-m-up-and-down-and-round-and-round/ncert-solutions/exercise-5-6
dateModified: 2026-10-07T15:44:30+00:00
---

# NCERT Solutions for Class 9 Maths Chapter 5 Exercise 5.6

Chapter 5: I’m Up and Down, and Round and Round. Every question from Exercise 5.6, 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 5.6

### Question 1

*3 marks · Short answer*

In a circle with centre O, the central angle AOB is $60^\circ$. If the radius of the circle is $12\text{ cm}$, what is the length of the chord AB?

**Solution**

1. Given: radius $OA = OB = 12\text{ cm}$, central angle $\angle AOB = 60^\circ$.
2. In $\triangle OAB$, $OA = OB$, so $\angle OAB = \angle OBA$.
3. Since $\angle AOB = 60^\circ$, the sum of the remaining two angles is $180^\circ - 60^\circ = 120^\circ$.
4. Thus, $\angle OAB = \angle OBA = \frac{120^\circ}{2} = 60^\circ$, making $\triangle OAB$ an equilateral triangle.
5. Therefore, the length of the chord $AB = OA = OB = 12\text{ cm}$.

**Answer:** 12 cm

> Common mistake: Assuming chord length is equal to radius without proving the triangle is equilateral.

### Question 2

*3 marks · Case-based*

Let A and B be two points on a circle with centre O. (i) Are there points X, Y on the circle, on the same side of AB, such that $\angle AXB$ is different from $\angle AYB$? (ii) Is it true that if $\angle AXB = \angle AYB$, then X and Y lie on the same side of the circle? (iii) If $\angle AXB = \angle AYB$, and X and Y do not lie on the circle, does the circle through A, B and X also pass through Y?

**Part (i)**

1. Angles in the same segment of a circle are equal.
2. Therefore, for any points X and Y on the circle on the same side of AB, $\angle AXB = \angle AYB$.
3. Thus, there are no such points where the angles are different.

Answer (i): No

**Part (ii)**

1. If $\angle AXB = \angle AYB$, then X and Y subtend equal angles at the circumference from the chord AB.
2. By the properties of arcs and angles, X and Y must lie on the same arc segment of the circle.
3. Therefore, it is true that they lie on the same side of the circle.

Answer (ii): Yes

**Part (iii)**

1. If X and Y do not lie on the circle, equality of angles $\angle AXB = \angle AYB$ only implies that A, B, X, Y are concyclic.
2. The circle passing through A, B and X is unique by Theorem 1.
3. Since Y does not lie on the circle initially, the circle through A, B and X does not necessarily pass through Y unless Y is on that circle.

Answer (iii): No

**Answer:** (i) No, (ii) Yes, (iii) No

> Common mistake: Confusing points on the circle with points outside the circle.

### Question 3

*3 marks · Short answer*

Find $x$ in Fig. 5.26.

**Solution**

1. Consider the cyclic quadrilateral formed by the four points on the circle in Fig. 5.26.
2. The angle opposite to the angle measuring $100^\circ$ is $x$.
3. The sum of opposite angles of a cyclic quadrilateral is $180^\circ$, so $x + 100^\circ = 180^\circ$.

**Answer:** $80^\circ$

> Common mistake: Confusing the opposite angles of a cyclic quadrilateral.

## 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 5.2](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)

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