I construct two files about tangent circle script tool.
You can use these script tools to make your own tangent circles on. Clicking below.

Tangent Circle 1

Tangent Circle 2


My Discovery for Tangent Circle

While investigating for Tangent Circle 2, I found an interesting fact.


When I fix tangent points of both given circles and move one given circle center (the point B in the picture below), the tangent circle center (the point D) is on one line.

On the graph below, I trace the center of the tangent circle with red color.


The line of the tangent circle center goes throgh the center of one given circle that is fixed (the point O above).

Even if I change the lenghs of radius, the line of the tangent circle center does not change.

This means the slope of this line (ED/OE) is constant.

The slope of this line depens only on where the tangent point is.


You can check this fact by clicking here, the GSP file I construct.

If you move point C, B(one of given circle centers), or A (the radius of one given circle center), the red line of the tangent circle center comes up.

Try making various slopes of tangent circle center by changing the position of one of tangent points.

The discovery above was about the second tangent circle.

Then, how about the first tangent circle?

I show a picture saying the similar result, about the firlst one.


The tangent circle ceter in this case is also on one line.