#### Cases of
Tangent Circles

### Below, two original
circles are highlighted in black. The common tangent circle and
the locus of its center are highlighted in red. The locus of the
midpoint of the base of the isosceles triangle formed in the construction
is displayed in light blue. Click on each link to see an animation
of the locus. Pictures of the intersecting and disjoint circle
cases can be obtained through the links.

**Smaller circle
contained in a larger one.**

Smaller
circle is external to common tangent circle.

Smaller
circle is internal to common tangent circle.

**Intersecting
circles.**

**
**Click
on the animation buttons to see two different common tangents.

**Disjoint circles.**

One of the
common tangent circles.

The other
common tangent circle.