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In this letter, a power-control scheme for maximum sum-rate is proposed for the fading multiple access channels by considering the presence of primary users. Both the average transmit-power constraints and the peak interference-temperature constraints are considered. The interference caused by cognitive users must be under a pre-specified threshold for protecting primary users. The power-control optimization is considered as a novel geometrical problem which investigates the relationship of positions of a line and a few points. At most two users transmit simultaneously for optimality and the corresponding conditions are provided for both cases. Based on the analysis, the optimal power control is given for each specific fading state. For lowering computational complexity, the power-control optimization problem is divided into two categories according to different tight constraints. Simulation results are provided for the optimal power-control performance.