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Sensor networks usually operate under very severe energy restrictions. Therefore, sensor communications should consume the minimum possible amount of energy. White broadcasting is a very energy-expensive protocol, it is also widely used as a building block for a variety of other network layer protocols. Therefore, reducing the energy consumption by optimizing broadcasting is a major improvement in sensor networking. In this paper, we propose an optimized broadcast protocol for sensor networks (BPS). The major novelty of BPS is its adaptive-geometric approach that enables considerable reduction of retransmissions by maximizing each hop length. BPS adapts itself and gets the best out of existing radio conditions. In BPS, nodes do not need any neighborhood information, which leads to low communication and memory overhead. We analyze the worst-case scenario for BPS and show that the number of transmissions in such a scenario is a constant multiple of those required in the ideal case. Our simulation results show that BPS is very scalable with respect to network density. BPS is also resilient to transmission errors.