Line $\ell $ intersects the plane $a$. It is known that in this plane there are $2011$ straight lines equidistant from $\ell$ and not intersecting $\ell$. Is it true that $\ell$ is perpendicular to $a$?
Problem
Source: 2011 Oral Moscow Geometry Olympiad grades 10-11 p2
Tags: 3D geometry, geometry, lines, Plane
