In this paper, we solve three geometric problems, including the ranking, convex hull and closest pair problems, under the broadcast communication model. To solve these problems, we propose a general scheme, the p-division approach, which is based upon the divide-and-conquer strategy. In the 2-dimensional space, the time complexities of our algorithms for solving these problems are all 
, where n is the number of input points and p is the number of processors used. Furthermore, our algorithms are all conflict-free and optimal. In the k-dimensional space, k≧3, our ranking algorithm requires 
time.