NCERT Solutions for Class 9 Maths Chapter 9 Circles Ex 9.1
NCERT Solutions for Class
9 Maths Chapter 9 Circles Ex 9.1 are the part of NCERT Solutions for Class 9 Maths. In this post, you will find the NCERT Solutions for Chapter 9 Circles Ex 9.1.
Ex 9.1 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 ΔMON and ΔPO’Q, we have
MO = PO’ [radii of congruent circles]
NO = QO’ [radii of congruent circles]
MN = PQ [given]
ΔMON = ΔPO’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 9.1 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 ΔMON and ΔPO’Q, we have
MO = PO’ [radii of congruent circles]
NO = QO’ [radii of congruent circles]
∠MON = ∠PO’Q [given]
∴ ΔMON ≅ ΔPO’Q [by SAS congruence rule]
∴ MN = PQ [by CPCT]
Hence Proved.
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