Jean-Pierre Ehrmann, Some geometric constructions,
Forum Geometricorum, 6 (2006) 327--334.

Abstract: We solve some problems of geometric construction. Some of them cannot be solved with ruler and compass only and require the drawing of a rectangular hyperbola: (i) construction of the Simson lines passing through a given point, (ii) construction of the lines with a given orthopole, and  (iii) a problem of congruent incircles whose analysis leads to some remarkable properties of the internal Soddy center.

[ps file][pdf]