On Wendel’s equality for intersections of balls

Abstract We study the analogue of Wendel’s equality in random polytope models which hull points is formed by intersections congruent balls, called spindle (or hyper-) convex hull. According to classical identity Wendel probability that origin contained (linear) n i.i.d. distributed according an symmetric distribution d -dimensional Euclidean space $$\mathbb {R}^{d}$$ R d assigns measure zero hyperplanes a constant depending only on and . While case one gets nonzero probabilities for $$n\ge d+1$$ n ≥ + 1 , this happens all 2$$ 2 question uniform normally models.