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How to Construct a Tangent to a Circle(With Steps & Pictures)

construct a tangent to a circle

This post is also available in: हिन्दी (Hindi)

A tangent of a circle is the line that touches the circle at only one point. You can draw only one tangent at a point to a circle. The point at which the tangent touches the circle is called the point of tangency(or the point of contact). The tangent and the radius of a circle are perpendicular to each other at the point of tangency(or point of contact).

Let’s understand how to construct a tangent to a circle with steps.

construct a tangent to a circle
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Maths can be really interesting for kids

How to Construct a Tangent to a Circle?

To construct a tangent to a circle, one should keep in mind these properties of tangents.

  • A tangent touches a circle at only one point.
  • A tangent is a line that never enters the circle’s interior.
  • The tangent touches the circle’s radius at the point of tangency at a right angle.

For more on tangents read here.

The steps involved to construct a tangent to a circle are:

Step 1: Draw a circle with the required radius with centre $\text{O}.

construct a tangent to a circle

Step 2: Join centre of the circle $\text{O}$ and any point $\text{P}$ on the circle. $\text{OP}$ is the radius of the circle.

construct a tangent to a circle

Step 3: Draw a line perpendicular to radius $\text{OP}$ through the point $\text{P}$. This line will be a tangent to the circle at $\text{P}$.

construct a tangent to a circle

To know the steps to construct a perpendicular line see here.

Construction of Two Tangents from a Point Outside of the Circle

Following are the steps used to construct tangents to a circle from a point outside of the circle.

Step 1: Draw a circle with the required radius with centre $\text{O}.

construct a tangent to a circle

Step 2: Take a point $A$ outside the circle.

construct a tangent to a circle

Step 3: Join points $\text{A}$ and $\text{A}$, and bisect the line $\text{AO}$. Let $\text{P}$ be the midpoint of $\text{AO}$.

construct a tangent to a circle

Step 4: Draw a circle taking $\text{P}$ as centre and $\text{PO}$ as a radius. This circle will intersect at two points $\text{B}$ and $\text{C}$ on the circle with centre $\text{O}$.

construct a tangent to a circle

Step 5: Join point $\text{A}$ with $\text{B}$ and $\text{C}$. $\text{AB}$ and $\text{AC}$ are the required tangents through points $\text{B}$ and $\text{C}$ on the circle.

construct a tangent to a circle

Let us see if the line segments $\text{AB}$ and $\text{AC}$ constructed are actually tangents to the circle with centre $\text{O}$ from the point $\text{A}$ or not.

Join $\text{B}$ with $\text{O}$. Observe that $\text{AO}$ is the diameter of the circle with centre $\text{P}$. Therefore, by construction, $\angle \text{ABO}$ is an angle in a semi-circle.

construct a tangent to a circle

Thus, $\angle \text{ABO} = 90^{\circ}$.

Since $\text{OB}$ is the radius of the circle with centre $\text{O}$, $\text{AB}$ has to be the tangent through the point $\text{B}$.

Similarly, $\text{AC}$ is the tangent through the point $\text{C}$.

Types of Coordinate Systems

Practice Questions

  1. What is the tangent to a circle?
  2. What are the properties of a tangent to a circle?
  3. How many tangents can you draw from a point lying on the circle?
  4. How many tangents can you draw from a point lying outside the circle?

FAQs

Can you construct a tangent from a point inside the circle?

No, we cannot construct a tangent from a point inside the circle. Any line drawn from a point inside the circle always crosses the circle at two points and such a line is called the secant of a circle.

How many tangents can be drawn from a point lying on a circle?

construct a tangent to a circle

We can draw only one tangent from a point lying on a circle.

How many tangents can be drawn from a point lying outside a circle?

construct a tangent to a circle

We can draw two tangents from a point lying outside a circle and these two tangents are always equal.

Conclusion

A tangent of a circle is the line that touches the circle at only one point. In this article, you understand how to construct a tangent to a circle. You can draw 

  • only one tangent from a point lying on the circle
  • two equal tangents from a point lying outside the circle
  • zero tangent from a point lying inside the circle

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