Geometric

I really need help with this question. I appreciate any help, please!
A diagram with a circle C1, with center O and radius r, and any point P.

The circle C2 has center P and radius OP. Let A be one of the points of intersection of C1 and C2. Circle C3 has center A, and radius r. The point P’ is the intersection of C3 with (OP).
Let r=1. Use an analytic approach to find OP’, when OP=2, OP=3 and OP=4. Describe what you notice and write a general statement to represent this