NCERT solutions for Class 9 Maths Chapter 10 Circles: Exercise 2
Question 1. Recall that two circles are congruent if they have the same radii. Prove that equal chords of congruent circles subtend equal angles at their centres.
Solution:
Given:
Two Congruent Circles C1 and C2
AB is the chord of C1
and PQ is the chord of C2
AB = PQ
To Prove: Angle subtended by the Chords AB and PQ are equal i.e. ∠AOB = ∠PXQ
Proof:
In â–³AOB & â–³PXQ
AO = PX (Radius of congruent circles are equal)
BO = QX (Radius of congruent circles are equal)
AB = PQ (Given)
â–³AOB â© â–³PXQ (SSS congruence rule)
Therefore, ∠AOB = ∠PXQ (CPCT)
Question 2. Prove that if chords of congruent circles subtend equal angles at their centres, then the chords are equal.
Solution:
Given:
Two Congruent circles C1 and C2
AB is the chord of C1 and PQ is chord of C2
& ∠AOB = ∠PXQ
To prove :
In â–³AOB and â–³PXQ ,
AO = PX (Radius of congruent circles are equal)
∠AOB = ∠PXQ (Given)
BO = QX (Radius of congruent circles are equal)
â–³AOB â© â–³PXQ (SAS congruence rule)
Therefore, AB = PQ (CPCT)
NCERT Solutions for Class 9 Maths Chapter 10 Circles
NCERT Solutions for Class 9 Maths Chapter 10 Circles is a curated article by professionals at GFG, to help students solve problems related to circles with ease. All the solutions provided here are factually correct and
The NCERT Class 9 Maths Chapter 10 Circles covered a variety of issues, including how to determine the separation between equal chords from the centre and the angles that a chord at a location subtended. There are also studies of cyclic quadrilaterals and their properties, as well as the angles that a circle’s arc subtends.
- Introduction to Circle
- Center of Circle
- Radius
- Chord
- Sector
- Segment
- Circumference
- Circle Theorems
- Cyclic Quadrilaterals
| Exercises under NCERT Solutions for Class 9 Maths Chapter 10 Circles |
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| NCERT Maths Solutions Class 9 Exercise 10.1 – 2 Questions & Solutions (2 Short Answers) |
| NCERT Maths Solutions Class 9 Exercise 10.2 – 2 Questions & Solutions (2 Long Answers) |
| NCERT Maths Solutions Class 9 Exercise 10.3 – 3 Questions & Solutions (3 Long Answers) |
| NCERT Maths Solutions Class 9 Exercise 10.4 – 6 Questions & Solutions (6 Long Answers) |
| NCERT Maths Solutions Class 9 Exercise 10.5 – 12 Questions & Solutions (12 Long Answers) |
| NCERT Maths Solutions Class 9 Exercise 10.6 – 10 Questions & Solutions (10 Long Answers) |