Define the tangent and its properties on a circle.
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Tangent at any point of circle is perpendicular to the radius through the point of contact...
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.