# NCERT Solutions for Class 9 Maths Exercise 10.2

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NCERT solutions for Class 9 Maths Circles

## NCERT Solutions for Class 9 Mathematics Circles

###### 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.

Ans. I Part: Two circles are said to be congruent if and only if one of them can be superposed on the other so as to cover it exactly.

Let C (O, ) and C (O’, ) be two circles. Let us imagine that the circle C (O’, ) is superposed on C (O, ) so that O’ coincide with O. Then it can easily be seen that C (O’,) will cover C (O,) completely if and only if

Hence we can say that two circles are congruent, if and only if they have equal radii.

II Part: Given: In a circle (O, ), AB and CD are two equal chords, subtend AOB and COB at the centre.

To Prove: AOB = COD

Proof: In AOB and COD,

AB = CD[Given]

AO = CO[Radii of the same circle]

BO = DO [Radii of the same circle]

AOB COD [By SSS axiom]

AOB = COD [By CPCT]

Hence Proved.

NCERT Solutions for Class 9 Maths Exercise 10.2

###### 2. Prove that if chords of congruent circles subtend equal angles at their centres, then the chords are equal.

Ans. Given: In a circle (O, ), AB and CD subtend two angles at the centre such that AOB = COD

To Prove: AB = CD

Proof: : In AOB and COD,

AO = CO [Radii of the same circle]

BO = DO [Radii of the same circle]

AOB = COD [Given]

AOB COD [By SAS axiom]

AB = CD [By CPCT]

Hence proved.

## NCERT Solutions for Class 9 Maths Exercise 10.2

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