​Common Tangents and Tangent Circles

About Geometry Worksheet Assignment 10.5:                 

 

Assignment 10.5 is an introduction to common tangents and tangent circles.

 

Prerequisite Skills:  Name and identify tangents (Assignment 10.4).  Identify radii of circles (Assignment 10.1).

 

Definitions:  Circles that intersect at exactly one point are tangent circles.

 

                           A line that is tangent to two or more circles is a common tangent of the circles.

 

                           Tangent circles on the same side of a common tangent are internally tangent.  Tangent circles on opposite sides of a common tangent

                           are externally tangent.

 

                          An internal tangent is a common tangent to circles on opposite sides of the tangent.  An external tangent is a common tangent to circles on

                          the same side of the tangent.

 

Theorems:  If two circles are externally tangent, then the distance between their centers is the sum of the radii of the circles.  

                           If two circles are internally tangent, then the distance between their centers is the difference of the radii of the circles.