# Tangent Circles: an Exploration

### Assignment 7

### Erin Horst

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?

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