Explorations in Geometry

with the

Geometer’s Sketchpad

Exploration 18.

In this exploration, you will learn to construct a line that is externally tangent to two tangent circles and discover some realtionships about them. Tangent circles are often called "osculating", or kissing, circles in recreational math books.

1) Create a line segment that will serve as the segemnt joining the centers of the two circles.

2) Create a random point somewhere between these two end points to be the point where the two circles KISS.

3) Now use each endpoint as the center of a circle and create two tangent circles.

4) Create a line that contains the line segment above.

5) Now use a figure like the one above to help you figure out how to construct the common tangent to the figures. (It will probably help to draw the two radii from the centers to the points of tangency)

6) Now measure the length of the segment of the tangent between the two tangent points. Can you express this realtionship as a function of the two radii?

7) What else can you observe about this figure.

8) Write a brief paragraph and describe the relationships you have observed in this exploration.