How do I draw 3 colinear points only using a compass?

Question

I know this is indeed possible because of the Mohr–Mascheroni theorem, and I thought about something like drawing two circles and looking at their intersection (for the 3rd point) but I have no idea how to prove that these points are indeed colinear.

Any help would be appreciated!

Answer 1

Take two points, $A,B$. Draw the two circles with the segment $AB$ as a radius. The two circles intersect at points $C,D$. Draw the two circles with $CD$ as radius. They intersect at points $E,F$. $E,F$ are co-linear with $A,B$.