Click Here for a discussion about circles c1, c2, and c3.
Look at the image below. In our picture we have three circles
(c1, c2, and c3). I have constructed the picture, but I have hidden all
of the identifying objects that may have helped to determine any relationships
between the circles. Make any conjectures about the image. To confirm or
adjust your conjecture you may click on the link for a table of terms to
see a picture and a definition of the terms.
Click Here for
a discussion about circles c1, c2, and c3.
In the last image, we were able to observe some relationships
between the circles. Although it is nice to observe those important facts
about the image above, we need to see if the relationships change when we
change one of the variables. If this were to happen then our image would
not be able to prove anything about circles, it would merely be a nice picture.
The question is, then, what do you think will happen when point B travels
around the path of c1?
Click on the image to see what happens to the relationship
between the circles when point B travels around circle c1.
If you do not have GSP on your computer click
here for an explanation and to continue the investigation.