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.

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

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

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.