Maria Calvo and Vicente Munoz, The most inaccessible point of a convex domain,
Forum Geometricorum, 13 (2013) 37--52.

Abstract. The inaccessibility of a point p in a bounded domain D subset R^n is the minimum of the lengths of segments through p with boundary at bd D. The points of maximum inaccessibility I_D are those where the inaccessibility achieves its maximum. We prove that for strictly convex domains, I_D is either a point or a segment, and that for a planar polygon I_D is in general a point. We study the case of a triangle, showing that this point is not any of the classical notable points.

[ps file] [pdf]