NCERT Solutions for Class 9 Maths Exercise 10.3 Circles

Before proceeding exercise 10.3 which has only three questions, we have to understand theorem 10.3, 10.4 and 10.5 also. Theorem 10.3 says that if a perpendicular is drawn from the center of the circle to a chord. This perpendicular bisects the chord.

The term bisects means dividing into two equal halves. Students should know that the term BI at many places 2. Similarly, Theorem 10.4 is the converse of theorem 10.3. It says that the line drawn through the center of the circle to bisect a given chord must be perpendicular to the chord.

Students must have notice that right through the study of geometry most of theorems have their converse too. For example – In higher classes you could study the Pythagoras theorem and its converse also.

In this exercise we shall also learn that we need minimum three points to drawn a circle. It is to be noted that these three point must not be collinear. The word collinear means passing through the same straight line or line on the same straight line.

We should also learn how to draw a circle which passes through three non – collinear points. By drawing perpendicular bisectors through them. Based on the above discussions Theorem 10.5 states that only one circle can be drawn which passes through three given non – collinear points.

In addition to the above, we have to learn how to complete the circle given an arc of a circle. To draw a circle we need to know the center of the circle and the radius.

By using theorem 10.5 we can find both of them and draw the required circle. It will not be out of place to mention that student should carry the geometry box. In particular – the compass, a sharpened pencil and an eraser.

Because many times it has been observe that students tried to resort to these small items even in examination hall. Exercise 10.3 has just three question and you should not mind doing all the things.