Peter Yff, A family of quartics associated with a triangle,
Forum Geometricorum, 9 (2009) 165--171.

Abstract:  It is known that the envelope of the family of pedal lines  (Simson or Wallace lines) of a triangle ABC is Steiner's  deltoid, a three-cusped hypocycloid that is concentric with the  nine-point circle of ABC and touches it at three points. Also  known is that the nine-point circle is the locus of the  intersection point of two perpendicular pedal lines. This paper  considers a generalization in which two pedal lines form any  acute angle \theta. It is found that the locus of their  intersection point, for any value of \theta, is a quartic curve  with the same axes of symmetry as the deltoid. Moreover, the deltoid is the envelope of the family of quartics. Finally, it is  shown that all of these quartics, as well as the deltoid and the  nine-point circle, may be simultaneously generated by points on a  circular disk rolling on the inside of a fixed circle.

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