NCERT Solutions for Class 9 Maths Chapter 10 Circles Ex 10.2

These NCERT Solutions for Class 9 Maths Chapter 10 Circles Ex 10.2 Questions and Answers are prepared by our highly skilled subject experts.

NCERT Solutions for Class 9 Maths Chapter 10 Circles Exercise 10.2

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:
Given: C₁ and C₂ are two congruent circles whose centres are O and P respectively.
Chord AB of circle C₁ is equal to the die chord QR of circle C₂.

To prove that ∠O = ∠P
Proof: In ∆OAB and ∆PQR.
OA = PQ (Radii of the congruent circle)
OB = PR (Radii of congruent circle)
AB = QR (Given)
By S-S-S- congruency condition,
∆OAB ≅ ∆PQR
∴ ∠O = ∠P (By CPCT)

Question 2.
Prove that if chords of congruent circles subtend equal angles at their centres, then the chords are equal.
Solution:
Given: C₁ and C₂ are two congruent circles whose centres are O and O’ respectively and ∠AOB = ∠PO’Q.
To prove that: AB = PQ

Proof: In ∆OAB and ∆O’PQ
OA = O’P (Radii of congruent circles)
OB = O’Q (Radii of congruent circles)
and ∠AOB = ∠PO’Q (Given)
By S-A-S congruency condition.
∠OAB = ∠O’PQ
∴ AB = PQ (By CPCT)