Question

Define the tangent and its properties on a circle.

Answer 1

Tangent:a line that intersect the circle at only one point.
and
Tangent at any point of circle is perpendicular to the radius through the point of contact...

Answer 2

A tangent to a circle is a line which intersects the circle at only one point.
The common point between the tangent and the circle is called point of contact.
Imagine a bicycle moving on a road. If we look at its wheel, we observe that it touches the road at just one point. The road can be considered as a tangent to the wheel.
It is to be noted that there can one and only one tangent through any given point on the circle.
Any other line through a point on the circle other than the tangent at that point would intersect the circle at two points. This can be easily seen from the following figure.

←→AB,←→CD,←→EF,←→GH,←→IJ are a few lines passing through the point P, where P is a point on the circle. We observe that all the lines except ←→AB pass through P and cut the circle at some other point. Hence, only ←→AB is a tangent and ←→CD,←→EF,←→GH and ←→IJ are secants to the circle.

Every secant has a corresponding chord to the circle. Therefore, a tangent can be considered as a special case of secant when the endpoints of its corresponding chord coincide.