COMMON EXTERNAL AND INTERNAL TANGENTS

What is a tangent to a circle?

The word tangent comes from the Latin word meaning "touching." This notion of touching is used in the geometrical meaning of tangent. Think of a wheel (circle) as tangent to a ramp (a line) as it rolls up or down the ramp. The wheel and the ramp are thought to have one point in common in a given plane. This is called the point of tangency.

A tangent to a circle is a line in the plane of a circle which intersects the circle in exactly one point. This point is called the point of tangency.

Consider the case when you have two circles.

Circles can be internally and externally tangent.

Two circles in the same plane are internally tangent if they intersect in exactly one point and the intersection of their interiors is not empty.

Two circles in the same plane are externally tangent if they intersect in exactly one point and their intersection of their interiors is empty.

Next, we want to discuss the cases when you have two circles and their respective common external and internal tangents.

A tangent of two circles is a common external tangent if the intersection of the tangent and the line segment joining the centers is empty.

For example, line AB and line CD are common external tangents.

A tangent of two circles is a common internal tangent if the intersection of the tangent and the line segment joining the centers is not empty.

For example, line EF and line GH are common internal tangents.

How many common external and internal tangents will the following sets of circles have?

Your answer should be NONE. Since the circles are not internally or externally tangent to begin with, Circles A and C and concentric circles E will not have any common internal or external tangents.

Lastly, we want to investigate all of the possible tangent cases to two given circles.

Click here for a demonstration for all of the possible INTERNAL TANGENT cases for two given circles.

Click here for a demonstration for all of the possible EXTERNAL TANGENT cases for two given circles.

Scripts have been made for common external and internal tangents.

Click here for common external tangent script.

Click here for common internal tangent script.

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