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NCERT Solutions for Class 9 Maths Chapter 10 Circles Ex 10.2

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

Ex 10.2 Class 9 Maths 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.
NCERT Solutions for Class 9 Maths Chapter 10 Circles Ex 10.2.1
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.

Ex 10.2 Class 9 Maths 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.
NCERT Solutions for Class 9 Maths Chapter 10 Circles Ex 10.2.2
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.

 

We hope the NCERT Solutions for Class 9 Maths Chapter 10 Circles Ex 10.2 help you. If you have any query regarding NCERT Solutions for Class 9 Maths Chapter 10 Circles Ex 10.2, drop a comment below and we will get back to you at the earliest.

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