# For any simple polygon in 2d and for any point in 2d there is always an edge of the polygon that is entirely visible from the point.

prove For any simple polygon in 2d and for any point in 2d there is always an edge of the polygon that is entirely visible from the point.

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What about taking a point on the plane non collinear with 2 consecutive vertices? The angle with vertex on this point is non zero. – Sigur Jan 29 '13 at 0:33

## 1 Answer

The statement is false. Consider, for instance, this polygon

and choose the origin as your point.

Even if you restrict to points outside the polygon, it is easy to modify the counterexample, e.g.

Your statement does hold for convex simple polygons, of course.

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