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In this paper we determine the optimal fractional frequency reuse (FFR) and resource allocation in OFDMA system. Since the users at the cell edge are more exposed to inter-cell interference therefore each cell is partitioned into two regions; inner region and outer region. We determine the optimal FFR factor for the outer region, bandwidth assigned to each region and subcarrier and power allocation to all the users in the cell. The problem is formulated as sum-power minimization problem subject to minimum rate constraints in both the regions. This is a mixed linear integer programming problem which is relaxed into a convex optimization problem. We develop an efficient algorithm by using Lagrange dual decomposition theory at reasonable computational cost.