Steve Butler, The lost daughters of Gergonne,
Forum Geometricorum, 9 (2009) 19--26.
Abstract: Given a triangle center we can draw line segments from each
vertex through the triangle center to the opposite side, this splits the
triangle into six smaller triangles called daughters. Consider the
following problem: Given a triangle S and a rule for finding a center
find a triangle T, if possible, so that one of the daughters of T, when using
the rule is S. We look at this problem for the incenter, median and