A Special Conic Associated with the Reuleaux Negative Pedal Curve
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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.
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