NCERT Solutions for Class 9 Maths Chapter 10 Circles Ex 10.3

NCERT Solutions for Class 9 Maths Chapter 10 Circles Ex 10.3 are part of NCERT Solutions for Class 9 Maths. Here we have given NCERT Solutions for Class 9 Maths Chapter 10 Circles Ex 10.3.

• Circles Class 9 Ex 10.1
• Circles Class 9 Ex 10.2
• Circles Class 9 Ex 10.3
• Circles Class 9 Ex 10.4
• Circles Class 9 Ex 10.5
• Circles Class 9 Ex 10.6

Board	CBSE
Textbook	NCERT
Class	Class 9
Subject	Maths
Chapter	Chapter 10
Chapter Name	Quadrilaterals
Exercise	Ex 10.3
Number of Questions Solved	3
Category	NCERT Solutions

NCERT Solutions for Class 9 Maths Chapter 10 Circles Ex 10.3

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.
Different pairs of circles are given below :
(i) Two points are common

(ii) One point is common

(iii) No point is common

(iv) No point is common

(v) One point is common

From figures, it is obvious that these pairs may have 0 or 1 or 2 points in common. Hence, a pair of circles cannot intersect each other at more than two points.

Question 2.
Suppose, you are given a circle. Give a construction to find its center.
Solution.

Steps of Construction

• Take three points P, Q, and R on the circle.
• Join PQ and
• Draw MT and NS, which are respectively the perpendicular bisectors of PQ and RQ and intersecting each other at a point 0. Hence, 0 is the center of the circle.

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

Given: Two circles with centers O and O’ intersect at two points M and N, so that MN is the common chord of the two circles and 00′ is the line segment joining their centers. Let OO’ intersects MN at P.
To prove: OO’ is the perpendicular bisector of MN.

 

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