**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.**

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.

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.

**NCERT Solutions for Maths Class 10**