A polygon has $n$ vertices, where $n\ge 3$. It has the following properties: * Every vertex of the polygon lies on the circumference of a circle $C$. * The centre of the circle $C$ is inside the polygon. * The radii from the centre of the circle $C$ to the vertices of the polygon cut the polygon into $n$ triangles of equal area.

For which values of $n$ are these properties sufficient to deduce that the polygon is regular?

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