MATHS CBSE IX| Chapter 10 - Circles|Exercise 10:3 Page 176 Q 3

MATHS CBSE IX| Chapter 10 - Circles|Exercise 10.3 Page 176 Q 2

 
Question 2:

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

Answer

The below given steps will be followed to find the centre of the given circle.

Step1. Take the given circle.

Step2. Take any two different chords AB and CD of this circle and draw perpendicular bisectors of these chords.

Step3. Let these perpendicular bisectors meet at point O. Hence, O is the centre of the given circle.

 
 
Question 3:

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

 

Answer

Consider two circles centered at point O and O’, intersecting each other at point A and B respectively.

Join AB. AB is the chord of the circle centered at O. Therefore, perpendicular bisector of AB will pass through O.

Again, AB is also the chord of the circle centered at O’. Therefore, perpendicular bisector of AB will also pass through O’.

Clearly, the centres of these circles lie on the perpendicular bisector of the common chord.

 

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