Ex 10.2 NCERT Solutions- Circles Class 9 Notes | EduRev

Mathematics (Maths) Class 9

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Class 9 : Ex 10.2 NCERT Solutions- Circles Class 9 Notes | EduRev

The document Ex 10.2 NCERT Solutions- Circles Class 9 Notes | EduRev is a part of the Class 9 Course Mathematics (Maths) Class 9.
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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: 
We have a circle having its centre at O and two equal chords AB and CD such that they subtend ∠AOB and ∠COD respectively at the centre, i.e. at O.
We have to prove that ∠AOB = ∠COD
Now, in ΔAOB and ΔCOD, we have

Ex 10.2 NCERT Solutions- Circles Class 9 Notes | EduRev

AO = CO               [Radii of the same circle]
BO = DO               [Radii of the same circle]
AB = CD               [Given]
∴ ΔAOB ≌ ΔCOD              [SSS criterion]
⇒ Their corresponding parts are equal.
∴ ∠AOB = ∠COD
 

Question 2. Prove that if chords of congruent circles subtend equal angles at their centres, then the chords are equal.
 Solution:
We have a circle having its centre at O, and its two chords AB and CD such that
∠AOB = ∠COD
We have to prove that AB = CD

Ex 10.2 NCERT Solutions- Circles Class 9 Notes | EduRev

∵ In ΔAOB and ΔCOD, we have:
AO = CO               [Radii of the same circle]
BO = DO               [Radii of the same circle]
∠AOB = ∠COD               [Given]
∴ ΔAOB ≌ ΔCOD              [SAS criterion]
∴ Their corresponding parts are equal, i.e. AB = CD


PERPENDICULAR FROM THE CENTRE TO A CHORD

REMEMBER

  • The perpendicular from the centre of a circle to a chord bisects the chord.
  • The line drawn through the centre of a circle to bisect a chord is perpendicular to the chord.
  • There is one and only one circle passing through three given non-collinear points.

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