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A Dubins car follows a Dubins path in $\mathbb{R}^2$, with constant wheel speed and limited turning radius. It is known that the shortest Dubins path in the absence of obstacles follows circular arcs ...

For any piece wise smooth, simple closed curve $\gamma$ in the Euclidean plane $E^2$ and fix a point $G$ inside the area circled by $\gamma$. Show: There exists three points $A,B$ and $C$ on the $\...