Partitioning the plane

You are given the coordinates of 4*K+5 points on a plane such that no three of them are collinear. You need to select five points from these : a central point O and four arm points A,B,C,D such that: - Rays from the centre to the arm points divide the plane into four regions containing an equal number of points - None of the four central angles is a reflex angle - Sum of absolute values of the cot