# Tangent Of A Circle

Before understanding the concept of the tangent of a circle, let us understand about the circle and how the line intersects the circle in this article.

**Also, learn:**

## What is a Circle?

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.

## What is the Tangent of a Circle?

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 or non-touching.

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

(1) Line [latex]AB[/latex] intersects the circle at two points [latex]P[/latex] and [latex]Q[/latex]. Such a line is called *secant* of the circle. [latex]P[/latex] and [latex]Q[/latex] are the points on the circle; [latex]PQ[/latex] is a chord of the circle.

(2) Line [latex]AB[/latex] touches the circle exactly at one point, [latex]P[/latex]. Such a line is called the *tangent* to the circle.

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

### 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.

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.

[latex]\overleftrightarrow{AB}, \overleftrightarrow{CD}, \overleftrightarrow{EF}, \overleftrightarrow{GH}, \overleftrightarrow{IJ}[/latex] are a few lines passing through the point [latex]P[/latex], where [latex]P[/latex] is a point on the circle. We observe that all the lines except [latex]\overleftrightarrow{AB}[/latex] pass through [latex]P[/latex] and cut the circle at some other point. Hence, only [latex]\overleftrightarrow{AB}[/latex] is a tangent and [latex]\overleftrightarrow{CD}, \overleftrightarrow{EF}, \overleftrightarrow{GH}~ and ~\overleftrightarrow{IJ}[/latex] 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.

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