## Circles

**Chapter 10**

**Exercise 10.2**

**EX 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:**

To Prove: ∠AOB = ∠CO’D

Proof: In ∆AOB and ∆CO’D

AB = CD [Given]

OA = O’C [Each equal to r]

OB = O’D [Each equal to r]

∴ ∆AOB ≅ ∆CO’D [ SSS congruence criteria]

⇒ ∠AOB = ∠CO’D [C.P.C.T.]

**EX 10.2 QUESTION 2.**

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

**Solution:**

To Prove: AB = CD

Proof: In ∆AOB and ∆CO’D,

OA = O’C [Each equal to r]

OB = O’D [Each equal to r]

∠AOB = ∠CO’D [Given]

∴ ∆AOB ≅ ∆CO’D [ SAS congruence criteria]

Hence, AB = CD [C.P.C.T.]