This is a Sangaku problem, featured on p. 70 of Paul Lockhart's book Measurement. See Lockhart introduce it.
Two circles lie on a line, touching each other at a point. A small circle is inscribed in the space between. How does its radius depend on the radii of the two larger circles?
Point A is free; Point B remains tangent to the ground and the circle defined by point A; Points and are dependent on A and B.