A convex polygon is such that the distance between any two vertices does not exceed 1.
(i) Prove that the distance between any two points on the boundary of the polygon does not exceed 1.
(ii) If X and Y are two distinct points inside the polygon, prove that there exists a point Z on the boundary of the polygon such that XZ \plus{} YZ\le1. inequalitiesconicsellipsegeometrycircumcircleinductionfunction