Broadcasting is one of the fundamental operations to disseminate information throughout a wireless network. Flooding is a simple method to realize broadcasting. However, flooding will incur a large number of redundant retransmissions, leading to low transmission efficiency, which is the ratio of the effective transmission area to the total transmission area. In this paper, we propose a geometry-based wireless broadcast protocol, called Optimized Broadcast Protocol (OBP), to improve the transmission efficiency. In OBP, each node calculates the retransmission locations based on a hexagon ring pattern in order to minimize the number of retransmissions, and only the nodes nearest to the calculated locations need to retransmit the broadcast packet. As shown by analysis, the transmission efficiency bound of OBP is 0.55, which is about 90% of the theoretical optimal bound 0.61 and is better than that of BPS, the geometry-based broadcast protocol with the highest transmission efficiency 0.41 known so far. Since the transmission efficiency is inversely proportional to the number of required nodes to cover a network area, in a static deployed network, the number of deployed nodes is minimized by OBP. However, in a randomly deployed network or a mobile network, when the node density is not high, the network area of interest may not be fully covered and OBP has worse reachability than BPS for some cases. We thus propose an extension of OBP, called OBPE, to improve the reachability when the node density is not high. We make comparisons for OBP, OBPE and BPS in terms of transmission efficiency, reachability, transmission redundancy, and the number of transmissions, energy consumption to show the advantages of OBP and OBPE.