I'm having some trouble with this, please help!

Let C be a circle with center (a/2,0) and radius a/2. Let l be the line with equation x=a. Find the polar equation of the curve produced in the following manner: for every angle theta, -pi/2 < theta < pi/2, consider the ray from the origin that makes the angle theta with the positive x-axis. This ray intersects C at a point A and l at point B and let O be the origin. Then the point P on the ray is on the curve if the segment OP = the segment AB.

I can see what the curve looks like (sort of an exponential line) but I cannot figure out how to find the equation for it. thanks for the help!!