वृत्त की स्पर्श रेखा

A circle is a set of all points in a plane which are equally spaced from a fixed point. The fixed point is called the center of the circle and the distance between any point on the circle and its center is called the radius.

Definition

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 are called the point of contact.

Given, a line to a circle could either be intersecting, non-intersecting or just touching the circle.

Consider any line $AB$ and a circle. There are 3 possibilities as shown below:

(1) Line $AB$ intersects the circle at two points $P$ and $Q$ . Such a line is called secant of the circle. $P$ and $Q$ are the points on the circle. $PQ$ is a chord of the circle.

Fig. 1

(2) Line $AB$ touches the circle exactly at one point $P$ . Such a line is called the tangent to the circle.

Fig. 2

(3) Line $AB$ does not touch the circle at any point and is referred to as a non-intersecting line.

Fig. 3

Tangent of a Circle Example

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.

Fig. 4

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 5.

Fig. 5

$AB,CD,EF,GH,IJ$ 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 $CD,EF,GH,IJ$ 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. Tangent of a circle