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The Negative Pedal Curve of the Reuleaux Triangle w.r. to a point $M$ on itsboundary consists of two elliptic arcs and a point $P_0$. Interestingly, theconic passing through the four arc endpoints and by $P_0$ has a remarkableproperty: one of its foci is $M$. We provide a synthetic proof based onPoncelet's polar duality and inversive techniques. Additional intriguingproperties of Reuleaux negative pedal are proved using straightforwardtechniques.

A Special Conic Associated with the Reuleaux Negative Pedal Curve