Bihar Board Class 9th Maths Solutions Chapter 10 Circles Ex 10.2 Textbook Questions and Answers.
BSEB Bihar Board Class 9th Maths Solutions Chapter 10 Circles 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:
Given : AB and CD are two equal chords of a circle with centre at O.
To prove : ∠AOB = ∠COD.
Proof:
In As AOB and COD, we have
AO = CO [Radii of the same circle] BO = DO [Radii of the same circle] and, AB = CD [Given]
∴ By SSS criterion of congruence, we have
∆ AOB ≅ ∆ COD
⇒ ∠AOB = ∠COD [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 : AB and CD are two chords such that angles subtended by these chords at the centre of the circle are equal.
i.e., ∠AOB = ∠COD
To prove : AB = CD
Proof : In As AOB and COD, we have
AO = CO [Radii of the same circle]
BO = DO [Radii of the same circle]
and, ∠AOB = ∠COD
∴ By SAS criterion of congruence, we have
∆ AOB ≅ ∆ COD
⇒ AB = CD [C.P.C.T.]