We are given a ruler with two marks at a distance 1. With its help we can do all possible constructions as with a ruler with no measurements, including one more: If there is a line $l$ and point $A$ on $l$, then we can construct points $P_1,P_2\in l$ for which $AP_1=AP_2=1$. By using this ruler, construct a perpendicular from a given point to a given line.
Problem
Source: VII International Festival of Young Mathematicians Sozopol 2016, Theme for 10-12 grade
Tags: construction, constructive geometry, geometry