How to make a geographic map that saves distances?

Question

Google Maps

Interested in the possibility of creating a map that would save distances. (We are talking about a static map that could be printed out)
It is clear that the distances between all points will not be saved, but it is possible to save the correct distance from a pre-selected point to any other point on the map.
Are there resources/programs that can do this?
Has anyone solved this problem on their own?
upd.
Found here the projection you need The question of obtaining a map remains.

Answer 1

Do you want to print and measure distances with a ruler? Then this choice is not a map, but a projection. Take QGIS, and there is a flat UTM projection. Yes, the tiles will look ugly, so it's better to look in the direction of vector data.