Circle in a Square

Let O be the center point of a circle with a radius of r. Inversion is defined as projecting point P into point P' so that O, P and P' are on the same halfline starting at O, and |OP| / r = r / |OP'|. For example, if r = 4, then (0,1) is projected to be (0,16), and (2,0) becomes (8,0).

For r = 1, find the projections of

a. point (1,1).
b. line y = ½
c. circle with radius of 2 and center point (1,0)
d. square with corners (1,1), (1,-1), (-1,1), (-1,-1).