In this exploration, we want to look tangent circles. Now, I must admit that i am not familiar with these kinds of circles. Therefore, I will start with an explantion of my construction and then leave some nice GSP files for YOU to play with.

Ok, so below i have a constructed a triangle with three noncollinear points and drew three circles, one centered about each point and each one tangent to the other two.

The contact triangle a'b'c' of triangle ABC is derived from the pairwise points of tangency of the three circles.

Here are some GSP of tangent circles.

NOTE: The incircle is tangent to the nine-point circle.