Point of Tangency: Definition & Example

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  • 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
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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

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