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For a positive integer $n$, an $n$-sided polygon lying on a circular arc or,shortly, an $n$-fan is a sequence of $n+1$ points on a circle goingcounterclockwise such that the "total rotation" $\delta$ from the first pointto the last one is at most $2\pi$. We prove that for $n\geq 3$, the $n$-fancannot be constructed with straightedge and compass in general from its centralangle $\delta$ and its central distances, which are the distances of the edgesfrom the center of the circle. Also, we prove that for each fixed $\delta$ inthe interval $(0, 2\pi]$ and for every $n\geq 5$, there exists a concrete$n$-fan with central angle $\delta$ that is not constructible from its centraldistances and $\delta$. The present paper generalizes some earlier resultspublished by the second author and \'A. Kunos on the particular cases$\delta=2\pi$ and $\delta=\pi$.

Geometric constructibility of polygons lying on a circular arc