We present a protocol, named RadGRPM, which runs on a distributed Delaunay triangulation of a set of nodes in Euclidean space. Given coordinates of the source node and a radius, RadGRPM multicasts a message to all nodes within the given radius from the source. Since the target nodes are all within a spherical region centered at the source, RadGRPM provides a special kind of geocast, which we call radius geocast. A multicast tree is not explicitly maintained in RadGRPM. Each node determines the next-hop nodes to forward a message solely using local information (the coordinates of its neighbors) together with the radius and coordinates of the center carried in the message. We prove that RadGRPM delivers a message to all nodes within the given radius. RadGRPM is also efficient in the sense that very few nodes within the radius receive duplicate messages, and nodes outside the radius receive no message. Extensive experimental results are presented to investigate the performance and characteristics of RadGRPM. Furthermore, we show that RadGRPM can be combined with unicast greedy routing to provide geocast to any spherical region not centered at the source node.