Class 9 Maths Ganita Manjari Chapter 5 Exercise 5.6 Solutions ā€“ Iā€™m Up and Down, and Round and Round

The NCERT Solutions for Class 9 Maths Ganita Manjari Chapter 5 Exercise 5.5 ā€“ Iā€™m Up and Down, and Round and Round provide step-by-step explanations to help students understand and solve the questions given in this exercise. The solutions cover important mathematical concepts and are designed to make problem-solving easier and more systematic for Class 9 students.

Students can use these solutions to check their answers, understand the correct method of solving each question, and strengthen their understanding of the concepts covered in Exercise 5.5. The solutions are presented in a simple and easy-to-follow manner, making them useful for homework, revision, and exam preparation. A printable PDF of the solutions is also available for students who prefer to study offline.

Class 9 Maths Ganita Manjari Chapter 5 Exercise 5.6 Solutions ā€“ Iā€™m Up and Down, and Round and Round

NCERT Solutions for Class 9 Maths Chapter 5 Exercise Set 5.6

Exercise Set 5.6 focuses on angles subtended by arcs at the centre and at points on the circle.

Question 1. In a circle with centre O, the central angle AOB is 60Ā°. If the radius of the circle is 12 cm, what is the length of chord AB?

Answer:
OA = OB = 12 cm

āˆ AOB = 60Ā°

Triangle AOB has two equal sides OA and OB. Since the included angle is 60Ā°, the remaining angles are also 60Ā°.

So, Ī”AOB is an equilateral triangle.

Therefore:

AB = OA = OB = 12 cm

Final answer:
Chord AB = 12 cm

Question 2. 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 āˆ AXB is different from āˆ AYB?

Answer:
No.

Angles subtended by the same chord AB at points on the same segment of the circle are equal.

Final answer:
No, āˆ AXB and āˆ AYB will be equal.

(ii) Is it true that if āˆ AXB = āˆ AYB, then X and Y lie on the same side of the circle?

Answer:
If X and Y are on the same segment of the circle with respect to chord AB, then the angles are equal. However, equal angles can also occur in special geometric situations, so the statement needs the condition that X and Y lie on the same circle with A and B.

Final answer:
For points on the same circle, equal angles subtended by AB indicate that the points lie on the same segment.

(iii) If āˆ AXB = āˆ AYB, and X and Y do not lie on the circle, does the circle through A, B and X also pass through Y?

Answer:
If X and Y lie on the same side of AB and āˆ AXB = āˆ AYB, then A, B, X and Y are concyclic.

So, the circle through A, B and X will also pass through Y.

Final answer:
Yes, if X and Y are on the same side of AB.

Question 3. Find x in the given figure.

Answer:
From the figure, ABCD is a cyclic quadrilateral and one angle is 100Ā°.

Opposite angles of a cyclic quadrilateral add up to 180Ā°.

So:

x + 100Ā° = 180Ā°
x = 80Ā°

Final answer:
x = 80Ā°

NCERT Solutions for Class 9 Maths Chapter 5 - Related Links