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

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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.

## 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 $\text{O}. Step 2: Join centre of the circle$\text{O}$and any point$\text{P}$on the circle.$\text{OP}$is the radius of the circle. Step 3: Draw a line perpendicular to radius$\text{OP}$through the point$\text{P}$. This line will be a tangent to the circle at$\text{P}$. To know the steps to construct a perpendicular line see here. ## Construction of Two Tangents from a Point Outside of the Circle Following are the steps used to construct tangents to a circle from a point outside of the circle. Step 1: Draw a circle with the required radius with centre$\text{O}.

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

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

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 $\text{O}$.

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.

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.

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 $\text{C}$.

## 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? 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? 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