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.

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