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This paper presents a framework to solve the strategic bidding problem of participants in an electricity market cleared by employing the full AC Optimal Power Flow (ACOPF) problem formulation. Traditionally, the independent system operators (ISOs) leveraged DC Optimal Power Flow (DCOPF) problem formulation to settle the electricity market. The main quest of this work is to find what would be the challenges and opportunities if ISOs leverage the full ACOPF as the market-clearing Problem (MCP)? This paper presents tractable mathematical programming with equilibrium constraints for the convexified AC market-clearing problem. Market participants maximize their profit via strategic bidding while considering the reactive power dispatch of generation units. The equilibrium constraints are procured by presenting the dual form of the relaxed ACOPF problem. The strategic bidding problem with ACOPF-based MCP improves the exactness of the location marginal prices (LMPs) and profit of market participants compared to the one with DCOPF. It is shown that the strategic bidding problem with DCOFP-based MCP is unable to model the limitations of reactive power support. The presented results display cases where the proposed strategic bidding method renders $52.3\%$ more profit for the Generation Company (GENCO) than the DCOPF-based MCP model. The proposed strategic bidding framework also addresses the challenges in coupling real and reactive power dispatch of generation constraints, ramping constraints, demand response implications with curtailable and time shiftable loads, and AC line flow constraints. Therefore, the presented method will help market participants leverage the more accurate ACOPF model in the strategic bidding problem.