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2011 lines equidistant from line and not intersecting it, plane related

Source: 2011 Oral Moscow Geometry Olympiad grades 10-11 p2

April 7, 2020
3D geometrygeometrylinesPlane

Problem Statement

Line ℓ\ell intersects the plane aa. It is known that in this plane there are 20112011 straight lines equidistant from ℓ\ell and not intersecting ℓ\ell. Is it true that ℓ\ell is perpendicular to aa?
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