Make a script tool for the construction of a tangent circle to two given circles.
Let us begin by visualizing what we are looking for.
We are given two circles
and want to construct a tangent circle to the two given circles, G and H. Now, how are we going to do this?
Let's start by constructing the diameter of the larger circle, G. Let's call this line j. Now, the center of our tangent circle T (still to be constructed) is going to lay on this line. Additionally, our tangent circle is tangent to G at point P.
Next, we are going to construct circle H, so that it will be centered on P.
Next, we will construct a segment from the center of circle H to Q. Then we will find the midpoint of segment QH and construct the perpendicular bisector. Then, where our perpendicular bisector intersects j, is the center of our tangent circle T.
Next, we construct an isoceles triangle highlighted in lavender, with vertices at the center of circle G, center of circle H, and Q. Then, finally, we construct our tangent circle with center T.
Since we have completed our construction, download the GSP script tool.
Explore tangent circles when the smaller circle is outside the large circle and when the smaller circle is centered on the large circle using the script tool. What happens? Are there other interesting situations to explore? What happens then?