Problem 1. Construct with straightedge and compass the circle through point P that is orthogonal to circles c1 and c2. (The centers of the circles are O1 and O2.) WRITE BRIEFLY the main steps of your construction. You do not have to justify the steps, just make it clear what you did.
Problem 2. In this figure, line ED is tangent to the circle.
(a) What is the radius of the circle d centered at E that is orthogonal to circle c?
(b) Draw this circle into the figure as accurately as you can.
(c) State precisely what it means for these two circles to be orthogonal.
(d) State precisely what it means for A to be the inversion of B in circle d.
(e) Explain why, if circle d is orthogonal to circle c, that B must be the inversion of A in d. (You can quote needed theorems, except for this one, but state clearly definitions and "facts" that you use.)