Generating Point from Centroid of Polygon falls outside of it?

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I have a feature class of polygons within a geodatabase and I'm trying to generate points based on the centroid of the polygon using the Feature to Point tool in ArcGIS 9.3.

However, I end up with several points that fall just outside of the polygon.

Is this the wrong tool to be using for this application?

Also, am I making the wrong assumption about this tool generating points from the centroids of polygons?



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