I have two related tasks. How is it possible to solve them (or at the at least the first one, which is the principle task) in ArcGIS or QGIS ?

Task 1.

How to find a radius of a largest circle inscribed in a polygonal object (shapefile) with a random shape of the boundaries? Under such circle means a circle that touches the polygonal object at two or more points. (Any circle with larger radius will intersect sides of the polygonal object). Is it possible to solve this task in a vector?

If transform this task in a raster the question will be the following:

Task 2.

How to find for a group of cells of a raster (which represent the closed contour (a boundary) of a polygonal object from the first task which was put on a raster) a point (Latitude, Longitude) which lies at a maximum distance from all cells of this group and locates inside this closed contour? I need to determine the point’s coordinates and this “maximum distance”.

Are there any tools or scripts of this kind available in ArcGIS or QGIS?

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