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The point that the line touches the circle is called the point of tangency.

A line drawn from the center of the circle to the point of tangency, a radius, is always perpendicular to the tangent line.

Tangent segments of a circle from the same external point are congruent.

If you throw an object in a circular trajectory, it will travel on a path that is tangent to the circular trajectory. (Think of throwing a Frisbee)

 

rectangle sand colored box
rectangle sand colored boxrectangle sand colored boxrectangle sand colored box
rectangle sand colored box




A common tangent is when a lines or line segments are tangent to more than one circle at a time. 2, 3, and 4 above are common tangents.


1. Tangent to a circle

2. Four Common Tangents: 2 Externals and 2 Internals

3. Two Common Tangents: 2 Externals 

4. Three Common Tangents: 2 Externals and 1 Internal 

5. The line or line segments have the same external point​
person throwing frisbee demonstrates point of tangency
If line AB is tangent at A and line CB is 

tangent at C then 
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Transcript


Hi welcome to MooMooMath. Today we are going to look at tangents to a circle. So let’s just start here with our first diagram. What is a tangent to a circle? A tangent to a circle is a line that a circle in one place. The only way to touch a circle in one place is to be on the exterior of the circle. So this point (points at the line touching the circle) and this line is called tangent to the circle. Let’s look at some scenarios when you have two circles. OK I have two circles here and I would like to draw two tangents. These two circles have four possible tangent lines. You can draw a tangent to the circle up here. ( Draws a line at the top of the circle) and that is actually called an external tangent because it does not cross between, if you think of these as two little eyeballs, the line that would connect the two circles together. I can draw a second external tangent down here (draws a line at the bottom of the circle) making two external tangents. I can also draw some internal tangent. An internal tangent is a line that does cross the line that would connect the centers of the two circles. So here is an internal tangent and here is another internal tangent. So these two circles have four lines where they are tangent now what if the circles actually touch each other. If the circles touch each other how many points of tangent will you have? Well you can have the two external ( one on the top and one on the bottom) but it will only have one internal tangent, and the point of tangent will be where the circles touch. Now let’s look at the last scenario and that is when the circles overlap. I still have my external tangents, but I don’t have any internal tangents. So let’s look at the rules for tangents. So here they are. So here is the circle and the point of tangent is a red dot. You can have two externals if the circles overlap and two external and one internal if the circles are tangent to each other. Two externals and two internals if the circles don’t touch each other. I actually have a fifth scenario. You can have a point out here and two lines that are tangent to that circle through that point and these two segments are congruent to each other. I wanted to point that out. I call this the party hat rule because it looks like a party hat on a head and these two sides are congruent or equal to each other. Also if you draw a radius to that point of tangent it will be perpendicular which comes in to play when you start solving these. Hope this helped.

Examples of Tangents
A
C
B

Tangent of a Circle

What is Tangent of a Circle?

three circles demonstrating tangent of point
point of tangency
two line segment with common external point

A tangent of a circle is a line or line segment that intersects a circle at one point.

Here are some examples of tangents to a circle.

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