‘Off on a tangent circle’
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 circle’s 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?