Tangent Of A Circle


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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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