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[HM] Harmonic Circles?
Posted:
Feb 26, 2000 10:42 AM


Suppose W,X,Y,Z are collinear and WY/XY = WZ/XZ. Then, by definition, {Y,Z} are harmonic conjugates wrt {W,X}. Now remove the requirement that Y be collinear with W,X. Then, as is well known, the locus of Z satisying the equation is a circle. One might call it the harmonic circle of Y wrt {W,X}. However, these circles have interesting properties, so possibly they already have a name, perhaps in one of the classics of John Casey. Has someone encountered these circles in the literature?
Changing the subject, I thank some of you who responded to inquiries about H. C. Gossard (for whom the Gossard Perspector is named), "a fruitful theorem," and "Hirst inverse." Your contributions are acknowledged in the new Encyclopedia of Triangle Centers  ETC, at http://cedar.evansville.edu/~ck6/encyclopedia/ .



