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Install NowNCERT Solutions for Class 9 Maths Exercise 10.3 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. Draw different pairs of circles. How many points does each pair have in common? What is the maximum number of common points?**

**Ans. **From the figure, we observe that when different pairs of circles are drawn, each pair have two points (say A and B) in common. Maximum number of common points are two in number.

Suppose two circles C (O, ) and C (O’, ) intersect each other in three points, say A, B and C.

Then A, B and C are non-collinear points.

We know that:

There is one and only one circle passing through three non-collinear points.

Therefore, a unique circle passes through A, B and C.

O’ coincides with O and

A contradiction to the fact that C (O’, ) C (O, )

Our supposition is wrong.

Hence two different circles cannot intersect each other at more than two points.

NCERT Solutions for Class 9 Maths Exercise 10.3

**2. Suppose you are given a circle. Give a construction to find its centre.**

**Ans. Steps of construction**:

**(a)** Take any three points A, B and C on the circle.

**(b)** Join AB and BC.

**(c)** Draw perpendicular bisector say LM of AB.

**(d)** Draw perpendicular bisector PQ of BC.

**(e)** Let LM and PQ intersect at the point O.

Then O is the centre of the circle.

**Verification**:

O lies on the perpendicular bisector of AB.

OA = OB ……….(i)

O lies on the perpendicular bisector of BC.

OB = OC ……….(ii)

From eq. (i) and (ii), we observe that

OA = OB = OC = (say)

Three non-collinear points A, B and C are at equal distance from the point O inside the circle.

Hence O is the centre of the circle.

NCERT Solutions for Class 9 Maths Exercise 10.3

**3. If two circles intersect at two points, prove that their centres lie on the perpendicular bisector of the common chord.**

**Ans. Given**: Let C (O, ) and C (O’, ) be two circles intersecting at A and B. AB is the common chord.

**To prove**: OO’ is the perpendicular bisector of the chord AB.

**Construction**: Join OA, OB, O’A, O’B.

**Proof**: In triangles OAO’ and OBO’,

OA = OB [Each radius]

O’A = O’B [Each radius]

OO’ = OO’ [Common]

OAO’ OBO’ [By SSS congruency]

AOO’ = BOO’ [By CPCT]

AOM = BOM

Now in AOB, OA = OB

And AOB = OBA [Proved earlier]

Also AOM = BOM

Remaining AMO = BMO

AMO = BMO = [Linear pair]

OM AB

OO’ AB

Since OM AB

M is the mid-point of AB.

Hence OO’ is the perpendicular bisector of AB.

## NCERT Solutions for Class 9 Maths Exercise 10.3

NCERT Solutions for Class 9 Maths PDF (Download) Free from myCBSEguide app and myCBSEguide website. Ncert solution class 9 Maths includes text book solutions from Mathematics Book. NCERT Solutions for CBSE Class 9 Maths have total 15 chapters. 9 Maths NCERT Solutions in PDF for free Download on our website. Ncert Maths class 9 solutions PDF and Maths ncert class 9 PDF solutions with latest modifications and as per the latest CBSE syllabus are only available in myCBSEguide.

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AOB = OBA in ques 3 is written wrong

helpful ????

This is excellent for study