A very simple geometry analysis

I would like to describe a circle of radius r1 and center O1 in an offset polar coordinate system O2 from its center in terms of the original polar coordinates O1 attached to its center (as shown in attached figure) In other words, a point moves in a circular path with radius r1 and center (origin) O1. As the point moves on the path with an angle theta1 we'd like to describe its motion from an origin O2 such that d0 is the fixed distance between O1 and O2. (Fixed distance and angle as well as radius are in blue color) phi0 is the fixed angle between O2 with respect to O1. Find the simplest form of r2 and theta2: in terms of r1, theta1, d0 and phi0 Provide mathematical proof to your findings. (I already have a complicated solution to the problem)