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NCERT Solutions for Class 10 Maths Chapter 10 : Circles

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Chapter 10 : Circles

10.1 Introduction

You have studied in Class IX that a circle is a collection of all points in a plane which are at a constant distance (radius) from a fixed point (centre). You have also studied various terms related to a circle like chord, segment, sector, arc etc. Let us now examine the different situations that can arise when a circle and a line are given in a plane.

10.2 Tangent To A Circle

In the previous section, you have seen that a tangent* to a circle is a line that intersects the circle at only one point. To understand the existence of the tangent to a circle at a point, let us perform the following activities:
Activity 1 : Take a circular wire and attach a straight wire AB at a point P of the circular wire so that it can rotate about the point P in a plane. Put the system on a table and gently rotate the wire AB about the point P to get different positions of the straight wire

10.3 Number Of Tangents From A Point On A Circle

To get an idea of the number of tangents from a point on a circle, let us perform the following activity:
Activity 3 : Draw a circle on a paper. Take a point P inside it. Can you draw a tangent to the circle through this point? You will find that all the lines through this point intersect the circle in two points. So, it is not possible to draw any tangent to a circle through a point inside it

10.4 Summary

In this chapter, you have studied the following points :
1. The meaning of a tangent to a circle.
2. The tangent to a circle is perpendicular to the radius through the point of contact.
3. The lengths of the two tangents from an external point to a circle are equal.



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