Shape up or guard up

Discrete Mathematics Level 1

Suppose a museum in the shape of a polygon can be guarded by a single guard. Does this imply the museum is convex?

Details: A point \(P\) in the museum is visible to a guard if the line segment from the guard to \(P\) lies within the triangle (or along the boundary).

See Guarding a Museum for details on guarding a museum.

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