Show that any two points lying inside a regular gon can be joined by two circular arcs lying inside and meeting at an angle of at least
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Show that any two points lying inside a regular $n-$gon $E$ can be joined by two circular arcs lying inside $E$ and meeting at an angle of at least $\left(1 - \frac{2}{n} \right) \cdot \pi.$
Izvor: Međunarodna matematička olimpijada, shortlist 1989
Školjka 
gon 
can be joined by two circular arcs lying inside 