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 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 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 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.
NCERT Solutions for Maths Class 10