NCERT Solutions Class 9th Maths Chapter – 9 Circles Exercise 9.1

NCERT Solutions Class 9th Maths Chapter – 9 Circles

NCERT Solutions Class 9th Maths Chapter – 9 Circles

Chapter – 9

Circles

Exercise 9.1

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: Two congruent circles with centres O and O’ and radii r, which have chords AB and CD respectively such that AB = CD. To Prove: ∠AOB = ∠CO’D Proof: In ∆AOB and ∆CO’D, we have AB = CD [Given] OA = O’C [Each equal to r] OB = O’D [Each equal to r] ∴ ∆AOB ≅ ∆CO’D [By SSS congruence criteria] ⇒ ∠AOB = ∠CO’D [C.P.C.T.]

Question 2. Prove that, if chords of congruent circles subtend equal angles at their centres, then the chords are equal. Solution – Given: Two congruent circles with centres O & O’ and radii r which have chords AB and CD respectively such that ∠AOB = ∠CO’D. To Prove: AB = CD Proof: In ∆AOB and ∆CO’D, we have OA = O’C [Each equal to r] OB = O’D [Each equal to r] ∠AOB = ∠CO’D [Given] ∴ ∆AOB ≅ ∆CO’D [By SAS congruence criteria] Hence, AB = CD [C.P.C.T.]

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