NCERT Class 9 Maths Chapter 9 Circles Solutions
NCERT Class 9 Maths Chapter 9 Circles Solutions Exercise 9.1 Q.1. Recall that two circles are congruent if they have the same radii. Prove that equal chords of a congruent circle subtend equal angles at their centres . Ans: Given: AB and CD are two equal chords of congruent circles with centres O and O’ respectively. To Prove: ∠AOB= ∠CO’D Proof: In ∆AOB and ∆ OCD, OA = OC | Radii of congruent circles OB = OD | Radii of congruent circles AB = CD | Given ∴ ∆ OAB ≅ OCD | SSS Rule ∴ ∠AOB ≅ ∠ COD | c.p.c.t. ∴ ∠AOB= ∠ COD Q.2. Prove that if chords of congruent circles subtend equal angles at their centres, then the chords are equal. Ans: ∠ AOB and ∠ COD are the two equal angles subtended by the chords AB and CD of two congruent circles with centres O and O respectively. To Prove: AB = CD Prove: In ΔΟΑΒ and ∆OCD, OA = O’C | Radii of congruent circles OB = O’D | Radii of congruent circles ∠AOB = ∠CO’D | Given ∴ ΔΟΑΒ ≅ O’CD | SAS Rule ∴ AB = CD | c.p.c.t. Exer...