NCERT Solutions for Class 9 Maths Chapter 10 Circles Ex 10.2

# NCERT Solutions for Class 9 Maths Chapter 10 Circles Ex 10.2

## 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 the part of NCERT Solutions for Class 9 Maths. Here you can find the NCERT Solutions for 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 centres.

Solution.

Let MN and PQ are two equal chords of two congruent circles with centres O and O’ respectively.
We have, MN = PQ.
In Î”MON and Î”PO’Q, we have
MO = PO’  [radii of congruent circles]
NO = QO’  [radii of congruent circles]
MN = PQ   [given]
Î”MON = Î”PO’Q           [by SSS congruence rule]
So,
MON = PO’Q    [by CPCT]
Hence, equal chords of congruent circles subtend equal angles at their centres.
Hence proved.

Ex 10.2 Class 9 Maths Question 2.
Prove that if chords of congruent circles subtend equal angles at their centres, 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 centres O and O’ of the circles are equal.

To prove: MN = PQ
Proof: In Î”MON and Î”PO’Q, we have
MO = PO’              [radii of congruent circles]
NO = QO’              [radii of congruent circles]
MON  = PO’Q      [given]
Î”MON Î”PO’Q    [by SAS congruence rule]
MN = PQ                 [by CPCT]

Hence Proved.

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