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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
- What is the tangent to a circle?
- What are the properties of a tangent to a circle?
- How many tangents can you draw from a point lying on the circle?
- 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
Recommended Reading
- How to Construct a Perpendicular Line (With Steps & Examples)
- How to Construct Parallel Lines(With Steps & Examples)
- How To Construct a Line Segment(With Steps & Examples)
- What are Collinear Points in Geometry – Definition, Properties & Examples
- What is a Transversal Line in Geometry – Definition, Properties & Examples
- What are Parallel Lines in Geometry – Definition, Properties & Examples
- What is Concurrent lines in Geometry – Definition, Conditions & Examples
- What is Half Line in Geometry – Definition, Properties & Examples
- What is a Perpendicular Line in Geometry – Definition, Properties & Examples
- Difference Between Axiom, Postulate and Theorem
- Lines in Geometry(Definition, Types & Examples)
- What Are 2D Shapes – Names, Definitions & Properties
- 3D Shapes – Definition, Properties & Types
