An algorithmic solution:

1. Extract vertices of your polygon (white dots).
2. Draw circles of the desired distance around these vertices (red lines).
3. Where all circles overlap is the area you're looking for (yellow area).

In QGIS, for this last step convert the circles to lines (Menu Vector / Geometry Tools/Polygons to lines), than use Menu Processing / Toolbox / Split with lines, splitting the circle-polygons with these lines.

An algorithmic solution, to be used with QGIS or other software:

1. Extract vertices of your polygon (white dots).
2. Draw circles of the desired distance around these vertices (red lines).
3. Where all circles overlap is the area you're looking for (yellow area).

In QGIS, for this last step convert the circles to lines (Menu Vector / Geometry Tools/Polygons to lines), than use Menu Processing / Toolbox / Split with lines, splitting the circle-polygons with these lines.