Jharkhand Board JAC Class 9 Maths Solutions Chapter 10 Circles Ex 10.2 Textbook Exercise Questions and Answers.

## JAC Board Class 9th Maths Solutions Chapter 10 Circles Ex 10.2

Page-173

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.

Answer:

Given: AB = CD (Equal chords)

To prove: ∠AOB = ∠CO’D

Proof: In AAOB and ACO’D,

OA = O’C

OB = O’D

AB = CD

∴ ∆AOB ∆CO’D

(SSS congruence criterion)

Thus, ∠AOB ≅ ∠CO’D by CPCT.

i.e. Equal chords of congruent circles subtend equal angles at their centres.

Question 2.

Prove that if chords of congruent circles subtend equal angles at their centres, then the chords are equal.

Answer:

Given: ∠AOB = ∠CO’D (Equal angles)

To prove: AB = CD

Proof: In ∆AOB and ∆CO’D,

OA = O’C (Radii)

∠AOB = ∠CO’D (Given)

OB = O’D (Radii)

∴ ∆AOB ≅ ∆CO’D

(SAS congruence criterion)

Thus, AB = CD by CPCT.

If chords of congruent circles subtend equal angles at their centres, then the chords are equal.