**Stephani
Eckelkamp**

** **

**ÔOff on a tangent circleÕ **

** **

**Tangent Circles Cases:**

Script tool for creating these
tangent circles located in GSP

Locus of Centers (in
red) for the above tangent circles when animated.

**Notice that when the center of the circle
tangent to both circleÕs center is animated it creates an ellipse. Click on the different animation links
above to see the different cases.**

** **

**What happens to the ellipse when one of
the circles is smaller? Bigger?**

**What is the difference between the
ellipses in the cases seen above?**

**What do you suppose the envelope of lines
may look like?**

**We know that the locus of points creates
an ellipse. How does this relate
to the envelope of lines?**

** **

**Make a prediction then click here to see an animation.**

** **

**Do you suppose that all cases form an
ellipse? Can you manipulate the
construction to form something else.**

**Click here for a hint**

** **

** **

**Check your prediction here. What figure is formed and why?**

**Notice where the center of the tangent
circle is located, is it ever outside of the centers of the two original circles?**