NCERT Solutions for Class 9 Maths Chapter 10 Circles Ex 10.2 are part of NCERT Solutions for Class 9 Maths. Here we have given NCERT Solutions for Class 9 Maths Chapter 10 Circles Ex 10.2.
- Circles Class 9 Ex 10.1
- Circles Class 9 Ex 10.2
- Circles Class 9 Ex 10.3
- Circles Class 9 Ex 10.4
- Circles Class 9 Ex 10.5
- Circles Class 9 Ex 10.6
| Board | CBSE |
| Textbook | NCERT |
| Class | Class 9 |
| Subject | Maths |
| Chapter | Chapter 10 |
| Chapter Name | Quadrilaterals |
| Exercise | Ex 10.2 |
| Number of Questions Solved | 2 |
| Category | NCERT Solutions |
NCERT Solutions for Class 9 Maths Chapter 10 Circles Ex 10.2
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 centers.
Solution.
Let MN and PQ are two equal chords of two congruent circles with centers O and O’ respectively,
i.e. MN = PQ.
Δ MON and Δ PO’Q, we have
MO = PO’ [radii of congruent circles]
NO = QO’ [radii of congruent circles]
and MN = PQ [given]
Δ MON = Δ PO’Q [by SSS congruence rule]
So, ∠MON = ∠ PO’Q [by CPCT]
Hence, equal chords of congruent circles subtend equal angles at their centers.
Hence proved.
Question 2.
Prove that, if chords of congruent circles subtend equal angles at their centers, then the chords are equal.
Solution.
Given: MN and PQ are two chords of congruent circles such that angles subtended by these chords at the centers O and O’ of the circles are equal.
To prove : MN = PQ
Proof: In ∠MON apd ∠ PO’Q, we get
MO = PO’
NO = QO’
and ∠MON = ∠PO’Q
∴ By SAS criteria, we get
Δ MON ≅ APO’Q
Hence Proved.
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