**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 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 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 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.

**Related Links:**

**NCERT Solutions for Maths Class 10**

**NCERT Solutions for Maths Class 11**