A wireless sensor network is composed of a distributed collection of nodes which corporate in performing sensing, computation and communication tasks. Since sensor nodes operate on battery power, their communication range will decline as time passes. When the energy of the sensor nodes has declined to a level that they cannot communicate with each other, the network cannot be sustained and might be replaced by a new sensor network. However, the old sensors may have a lot of valuable data, and it is wise to retrieve as much information as possible from the old sensors. The maximum sensor reuse problem concerns deploying the new sensor network to maximize the number of old sensors that can communicate with the sensors in the newly deployed network. This paper proposes two new geometric concepts, network distance and network bisector, and uses them to solve the maximum sensor reuse problem. Specifically, the maximum sensor reuse problem can be solved in O(n2 log n) time if n existing sensors are to be considered.