Finding the center of an kissing circle

Question

I have three circles in the following graph:

Graph

What I want to do is get the upper circle to touch the other two circles, like so:

Touching Circle

What is the graph equation for what I'm looking for (red circle)?

Answer 1

$$x^2 + \left(y - \left(\sqrt{3}-1\right)\right)^2 = 1$$