NCERT Solutions for Class 9 Maths Exercise 10.2

NCERT Solutions for Class 9 Maths Exercise 10.2 book solutions are available in PDF format for free download. These ncert book chapter wise questions and answers are very helpful for CBSE board exam. CBSE recommends NCERT books and most of the questions in CBSE exam are asked from NCERT text books. Class 9 Maths chapter wise NCERT solution for Maths Book for all the chapters can be downloaded from our website and myCBSEguide mobile app for free.

NCERT solutions for Class 9 Maths Circles Download as PDF

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.

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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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