Arbelos

Draw three circles

Set the radii to be r, s, and r+s

Make the circles tangent in pairs

Draw a fourth circle and make it tangent to the previous three

Open the symbolic panel Type in radius(C3)

Draw another circle, tangent to the previous one, the outer circle and one of the initial inner circles.

Observe its radius, any guess as to a pattern?

Create another tangential circle.

Observe its radius. Do you see a pattern?

What do you guess the next radius in the sequence would be? Try it and see if you are correct.