Circle Centers Conjecture
This conjecture was based on observations made about the centers of the circles c1, c2 and c3.
Are there any connections between them?
This image shows us that one line passes throught the point
of tangency and the center of c1 and c3. This will help in our construction
of the tangent circle. Notice also that the line passing through the center
of c2 and its point of tangency does not pass through the center of the
circle.
In our next image, I have added the line that passes through the center
of circle c2 and through the center of the "proposed" tangent
circle. Make any observations you can about the image. You can click on
the image to explore the relationships using GSP, but it is not necessary.
This image shows us some connections between the circle c2 and the tangent circle c3.
Look specifically at the line that connects the centers of c2 and c3.
Click Here to continue this investigation.