Point of Tangency: Definition & Example

Point of Tangency: Definition & Example
Coming up next: Vertical Line Test: Definition & Examples

You're on a roll. Keep up the good work!

Take Quiz Watch Next Lesson
 Replay
Your next lesson will play in 10 seconds
  • 0:00 What Is a Point of Tangency?
  • 0:21 Point of Tangency on a Circle
  • 1:30 Point of Tangency To a Curve
  • 2:34 Lesson Summary
Add to Add to Add to

Want to watch this again later?

Log in or sign up to add this lesson to a Custom Course.

Log in or Sign up

Timeline
Autoplay
Autoplay
Speed

Recommended Lessons and Courses for You

Lesson Transcript
Instructor: Miriam Snare

Miriam has taught middle- and high-school math for over 10 years and has a master's degree in Curriculum and Instruction.

In this lesson, you will learn the definition of a point of tangency. You will also see a few different examples of where points of tangency can occur.

What Is A Point Of Tangency?

A tangent is an object, like a line, which touches a curve. The tangent only touches the curve at one point. That point is called the point of tangency. The tangent does not intersect (pass through) the curve. Let's look at two different examples of points of tangency that you may encounter in math.

Point Of Tangency On A Circle

In geometry, we talk about tangents to circles. To visualize what a line tangent to a circle looks like, imagine that you balance a ruler on a ball, as is pictured here:

Beachball with a tangent line

The ruler is the tangent. The red point where the ruler touches the ball is the point of tangency. Let's simplify the diagram to something you might see in a geometry book. The ball becomes a circle, and the ruler becomes a line, like this:

Circle with a tangent line

A single circle can have more than one point of tangency if it has more than one line 'balancing' on it. For example, if you put a square around a circle, then each side of the square has a point of tangency on the circle.

Circle inscribed in a square

Points A, B, C, and D in the diagram above are all points of tangency on the circle.

Lines or segments are not the only objects that can be tangent to a circle. You could have two circles that are tangent to one another. Think about two basketballs next to each other on a shelf.

Two basketballs

The green point where the two basketballs bump up against each other is the point of tangency. The same situation in a simplified geometry diagram would look like this:

Two tangent circles

To unlock this lesson you must be a Study.com Member.
Create your account

Register to view this lesson

Are you a student or a teacher?

Unlock Your Education

See for yourself why 30 million people use Study.com

Become a Study.com member and start learning now.
Become a Member  Back
What teachers are saying about Study.com
Try it risk-free for 30 days

Earning College Credit

Did you know… We have over 200 college courses that prepare you to earn credit by exam that is accepted by over 1,500 colleges and universities. You can test out of the first two years of college and save thousands off your degree. Anyone can earn credit-by-exam regardless of age or education level.

To learn more, visit our Earning Credit Page

Transferring credit to the school of your choice

Not sure what college you want to attend yet? Study.com has thousands of articles about every imaginable degree, area of study and career path that can help you find the school that's right for you.

Create an account to start this course today
Try it risk-free for 30 days!
Create An Account
Support