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.*


[![enter image description here][1]][1]


  [1]: https://i.sstatic.net/W9W9Q.png