ABSTRACT: Let M be a compact k-dimensional riemmanian manifold minimally immersed in the unitn-dimensional sphere S n . It is easy to show that for any p ∈ S n the boundary of the geodesic ball in S with radius π2 and center at p (in this case this boundary is an equator) must intercept the manifold M .When the codimension is 1 , i.e. k = n − 1 , it is known that the ricci curvature, is not greater than 1 .We will prove that if the ricci curvature is not greater than 1− α 2 n−2 , then the boundary of every geodesicball with radius cot −1 (α) must intercept the manifold M . We give examples of manifols for which theradius cot −1 (α) is optimal. Next, for any codimension, i.e. for any M k ⊂ S n , we find a number r 1 that depends only on n such that for any collection of n + 1 points {p i } n+1i=1 in S n that constitutes anorthonormal basis of R n+1 , the union of the boundaries of the geodesic balls with radius r 1 and center p i , i = 1,2,...n +1 , must intercept the manifold M . §1 Introduction and preliminaries.Let M be a compact, oriented minimal hypersurface immersed in the n-dimensional unitsphere S