Copy of Orthogonal Circles

If you have not encountered the term "orthogonal circles" before you can use this environment to figure out what the term could mean.[br][br]The black dots fix the centers of the circles - red & green dots fix the radii of the circles[br][br]If you add a fixed length, say d, to each of the radii of orthogonal circles and the distance between the centers, do the circles remain orthogonal?[br] [always, sometimes, never][br][br]If you multiply each of the radii of orthogonal circles and the distance between the centers by the same amount, say a, do the circles remain orthogonal?[br] [always, sometimes, never][br][br][br]Write an equation or a set of equations that relate the positions of the centers, the size of the radii and the location of the point(s) of intersection of the two circles.

Information: Copy of Orthogonal Circles