  Two generalizations of Hagge's theorems are described. In the first we
consider what happens when one moves from the orthocentre to a general point.
What one loses by doing so is the indirect similarity and hence one loses the
centre of indirect similarity. Instead one proceeds from the centre of the
circle under consideration. In the second generalization we consider pairs of
triangles that have orthologic centres with respect to each other, so that an
indirect similarity is the main feature preserved.
