Support straight line

Let \(F\) be a convex body in the plane and \(A\) a point in the boundary of \(F\). A support line of \(F\) in \(A\) is a line that passes through \(A\) such that \(F\) is contained in one of the closed half-spaces defined by that line.

In the figure, the line with direction \(l\) that goes through \(A\) is a support line of \(F\). The line with direction \(l\) that goes through \(B\) is also a support line of \(F\).

In this case the points \(A\) and \(B\) are not illuminated by direction \(l\).