Students can Download Class 9 Maths Chapter 12 Circles Ex 12.3 Questions and Answers, Notes Pdf, KSEEB Solutions for Class 9 Maths helps you to revise the complete Karnataka State Board Syllabus and to clear all their doubts, score well in final exams.
Karnataka State Syllabus Class 9 Maths Chapter 12 Circles Ex 12.3
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:
(1) Circles which do not intersect each other :
There is no common point for these circles.
(2) Circles which touch externally :
For these pairs of circles, there is only one common point ‘Y’.
(3) Circles which touch internally :
These pair of circles touch internally. These have common endpoint ‘X’.
(4) Intersecting Circles :
The above circle intersect each other at two points G and H.
∴ the circles have two points in common.
It can be observed that there can be a maximum of 2 points in common.
Consider the situation in which two congruent circles are superimposed on each other. This situation can be referred to as if we are drawing the circle two times.
Question 2.
Suppose you are given a circle. Give a construction to find its centre.
Solution:
If a circle with any measurement, to find out centre of circle, steps are as follows :
- Construct a circle with any radius.
- Draw two chords AB and CD with any length.
- Draw perpendicular bisector for AB and CD chords.
- If these bisectors intersect each other when produced they meet at ’O’. O is the centre of the circle.
Question 3.
If two circles intersect at two points, prove that their centres lie on the perpendicular bisector of the common chord.
Solution:
Two circles with centre A and B intersect at ‘C’ and ‘D’.
CD is the common chord for these circles.
To Prove: A and B centres are on bisector of CD.
Proof: Circle with centre ‘A’. CD is the chord.
CD meets B through ‘O’.
CD is the chord for circle centred B.
Now CD meet A through ‘O’.
Hence, If two circles intersect at two points, their centres lie on the perpendicular bisector of the common chord.