Tangent to a Circle

To understand the existence of the tangent to a circle at a point, let us perform
the following activity:

Activity : 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 [see Fig.].
In various positions, the wire intersects the
circular wire at P and at another point Q1 or Q2 or
Q3, etc. In one position, you will see that it will
intersect the circle at the point P only (see position
A′B′ of AB). This shows that a tangent exists at
the point P of the circle. On rotating further, you
can observe that in all other positions of AB, it will
intersect the circle at P and at another point, say R1
or R2 or R3, etc. So, you can observe that there is
only one tangent at a point of the circle.
Hope the above explanation helped you, now let us learn about line intersecting circle.