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We study a cognitive network consisting of a single primary transmitter and multiple secondary, or cognitive, users. The primary transmitter, located at the center of the network, communicates with primary receivers within a disc called the primary exclusive region (PER). Inside the PER, no cognitive users may transmit, in order to guarantee an outage probability for the primary receivers within. Outside the PER, uniformly distributed cognitive users may transmit, provided they are at a certain protected radius from a primary receiver. We analyze the aggregated interference from the cognitive transmitters to a primary receiver within the PER. Based on this interference and the outage guarantee, we derive bounds on the radius of the PER, showing its interdependence on the receiver protected distance and other system parameters. We also extend the analysis to allowing the cognitive users to scale their power according to the distance from the primary transmitter. These studies provide a closed-form, theoretical analysis of such a network geometry with PER, which may be relevant in the upcoming spectrum sharing actions.