ArcGIS or QGIS: how to check if a polygon fits inside another polygon?

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How do I check if one polygon fits inside another polygon? Furthermore how do I automatically check if one polygon fits in other polygons of my shapefile?

I have a shapefile with thousands of differnt polygons each one listed in the attribution list with its own ID. The polygons have a non-regualar shape. Now I want to check in which of those polygones fits one specific other polygone (it is a circle with a specific diametre). I only have a need for those polygones inside my shapefile in which this circle fits.

An idea was to have use the geometrical midpoint, overlay the circles and polygones midpoind and see if they edges overlay. Wrong idea since the geometrical midpoit is the wrong approch already. The polygons have very weird shapes, can be very long with a huge tip or whatever. Here the geometrical midpoint would be somewhere inside or even outside the long part of the polygone, the circle wouldn't fit, but at the tip it actually would fit.

Any idea how I can process automatically? Basically I just need to sort out those polygons in which my circle/other polygone doesn't fit. Don't care if the approch is for vector or raster (vector would be nice but I can always transform), for ArcGIS or QGIS.

KR, Knut



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