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Class 9th Science
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Class 9th Math
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Class 9 Social Science History: India and the Contemporary World ā I
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Class 9 Social Science Geography: Contemporary India ā I
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Class 9 Social Science Civics (Political Science): Democratic Politics ā I
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Class 9 Social Science Economics: Understanding Economic Development ā I
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Class 9 English Beehive
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Class 9 English Beehive Poem
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Class 9 English Moments
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Online Class For 9th Standard Students (CBSE) (English Medium)

### Exercise: 10.3 (Page No: 176)

1. Draw different pairs of circles. How many points does each pair have in common? What is the maximum number of common points?

Solution:

In these two circles, no point is common.

Here, only one point āPā is common.

Even here, P is the common point.

Here, two points are common which are P and Q.

No point is common in the above circle.

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

Solution:

The construction steps to find the center of the circle are:

Step I:Ā Draw a circle first.

Step II:Ā Draw 2 chords AB and CD in the circle.

Step III:Ā Draw the perpendicular bisectors of AB and CD.

Step IV:Ā Connect the two perpendicular bisectors at a point. This intersection point of the two perpendicular bisectors is the centre of the circle.

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

Solution:

It is given that two circles intersect each other at P and Q.

To prove:

OOā is perpendicular bisector of PQ.

Proof:

Triangle ĪPOOā and ĪQOOā are similar by SSS congruency since

OP = OQ and OāP = OQ (Since they are also the radii)

OOā = OOā (It is the common side)

So, It can be said that ĪPOOā ĪQOOā

ā“ POOā = QOOā ā (i)

Even triangles ĪPOR and ĪQOR are similar by SAS congruency as

POR = QOR (As POOā = QOOā)

OR = OR (Common arm)

So, ĪPOR ĪQOR

ā“ PRO = QRO

Also, we know that

PRO+QRO = 180Ā°

Hence, PRO = QRO = 180Ā°/2 = 90Ā°

So, OOā is the perpendicular bisector of PQ.