The document Ex 10.3 NCERT Solutions- Circles Class 9 Notes | EduRev is a part of the Class 9 Course Mathematics (Maths) Class 9.

All you need of Class 9 at this link: Class 9

**Question 1. Draw different pairs of circles. How many points does each pair have in common? What is the maximum number of common points? Solution:** Let us draw different pairs of circles as shown below:

We have

In figure | Maximum number of common points |

(i) | nil |

(ii) | one |

(iii) | two |

Thus, two circles can have at the most two points in common.

**Question 2. Suppose you are given a circle. Give a construction to find its centre. Solution:** Steps of construction

I . Take any three points on the given circle. Let these be A, B and C.

II. Join AB and BC.

III . Draw the perpendicular bisector PQ of AB.

IV. Draw the perpendicular bisector RS of BC such that it intersects PQ at O.

Thus, â€˜Oâ€™ is the required centre of the given circle.

**Question 3. If two circles intersect at two points, prove that their centres lie on the perpendicular bisector of the common chord. Solution: **We have two circles with centres O and O', intersect at A and B.

âˆµ AB is the common chord of two circles and OO' is the line segment joining the centres of the circles.

Let OO' and AB intersect each other at M.

âˆ´ To prove that OO' is the perpendicular bisector AB, we join OA, OB, O'A and O'B.

Now, in Î”OAO' and Î”OBO',

we have OA = OB [Radii of the same circle]

O'A= O'B [Radii of the same circle]

OO' = OO' [Common]

âˆ´ Using the SSS criterion,

Î”OAO'â‰Œ Î”OBO'

â‡’ âˆ 1= âˆ 2 [c.p.c.t.]

Now, in Î”AOM and Î”BOM,

OA = OB [Radii of the same circle]

OM = OM [Common]

âˆ 1= âˆ 2 [Proved]

âˆ´ Î”OAM â‰Œ Î”BOM [SAS criterion]

â‡’ âˆ 3= âˆ 4 [c.p.c.t.]

But âˆ 3 + âˆ 4 = 180Âº [Linear pair]

âˆ´ âˆ 3= âˆ 4 = 90Âº each.

â‡’ AM âŠ¥ OO'

Also AM = BM [c.p.c.t.]

â‡’ M is the mid-point of AB.

Thus, OO' is the perpendicular bisector of AB.

**EQUAL CHORDS AND THEIR DISTANCES FROM THE CENTRE**

**REMEMBER**

- The length of the perpendicular from a point to a line is the distance of the line from the point.
- A circle can have infinitely many chords.
- In a circle, the longer chord is nearer to the centre than the smaller chord.
- Diameter is the longest chord of a circle.
- Equal chords of a circle (or of congruent circles) are equidistant from the centre (or centres).
- Chords equidistant from the centre of a circle are equal in length.

192 videos|230 docs|82 tests

### What is a Circle?

- Video | 01:59 min
### What is an Arc? Major and Minor

- Video | 04:31 min
### Test: Angle Subtended By The Chord

- Test | 20 ques | 20 min
### Angle Subtended by an Arc of a Circle Theorems(Hindi)

- Video | 23:03 min
### Theorems Related to Chords of a Circle

- Video | 13:48 min
### What is a Segment of the Circle?

- Video | 02:16 min

- Basic Concepts of a Circles
- Video | 02:31 min
- Short Answer Type Questions- Circles
- Doc | 4 pages