We want to explore the GSP software today. We will dive into common tangents of two given circles. We want to make a script that we can use and we want to test it for all different cases. So first we want to have two given circles like below:

We now want to construct the common tangents to these two circles. So we want to make the it look like the picture below where the red circle is tangent to both of the given circles:

We now want to test it for all different cases. We can try if the smaller circle is outside and inside of the tangent circle. It will look like the following picture below:

Here is one more picture of what the smaller circle looks like when it is external to the tangent circle (blue).

We also want to find if the smaller circle is inside of the tangent circle. It will look like the following picture.

One last thing we want to determine is how to make a script for common tangents to two given circles. Just click here for the script. This will allow us to find the common tangents whether the smaller circle is outside or inside of the tangent circle.