Class 9 Maths Ganita Manjari Chapter 5 Exercise 5.2 Solutions ā€“ Iā€™m Up and Down, and Round and Round

Class 9 Maths Ganita Manjari Chapter 5 Exercise 5.2 Solutions explain why a chord and the centre of a circle form an isosceles triangle. These solutions also show how equal chord bases make two centre-chord triangles congruent by SSS.

Chapter 5, Iā€™m Up and Down and Round and Round Class 9, develops circle geometry through centre, radius, chord, equal chords and triangle congruence. Class 9 Maths Ganita Manjari Chapter 5 Exercise 5.2 Solutions focus on two proof-based questions. Both questions use one simple fact: all radii of the same circle are equal. These Class 9 Maths Chapter 5 Exercise 5.2 Solutions help students write exact geometry proofs for the triangle formed by chord and centre, equal base lengths and SSS congruence circle chord questions. Exercise Set 5.2 appears after the theorems on equal chords and angles at the centre.

Class 9 Maths Ganita Manjari Chapter 5 Exercise 5.2 Solutions ā€“ Iā€™m Up and Down, and Round and Round

Class 9 Maths Ganita Manjari Chapter 5 Exercise 5.2 Solutions

NCERT Solutions for Class 9 Maths Chapter 5 Exercise Set 5.2

Exercise Set 5.2 focuses on chords and the angles they subtend at the centre.

Question 1. Show that the triangle formed by a chord and the centre of the circle is isosceles.

Answer:
Let AB be a chord of a circle with centre O.

Join OA and OB.

Since A and B lie on the circle:

OA = radius
OB = radius

So:

OA = OB

Therefore, triangle OAB has two equal sides.

Final answer:
The triangle formed by a chord and the centre is isosceles.

Question 2. Show that if two such isosceles triangles have equal base length, they are congruent to each other.

Answer:
Let AB and CD be two equal chords of the same circle with centre O.

Consider triangles OAB and OCD.

OA = OC because both are radii.
OB = OD because both are radii.
AB = CD because the chord lengths are equal.

Therefore, by SSS congruence:

Ī”OAB ā‰… Ī”OCD

Final answer:
The two isosceles triangles are congruent by SSS congruence.

NCERT Solutions for Class 9 Maths Chapter 5 - Related Links