  The Negative Pedal Curve of the Reuleaux Triangle w.r. to a point $M$ on its
boundary consists of two elliptic arcs and a point $P_0$. Interestingly, the
conic passing through the four arc endpoints and by $P_0$ has a remarkable
property: one of its foci is $M$. We provide a synthetic proof based on
Poncelet's polar duality and inversive techniques. Additional intriguing
properties of Reuleaux negative pedal are proved using straightforward
techniques.
