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.]
