A rhombus is inscribed in the region common to the two circles \( x^2 + y^2 - 4x - 12 = 0 \) and \( x^2 - y^2 + 4x - 12 = 0 \) with two of its vertices on the line joining the centres of the circles. The area of rhombus is
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For symmetric circle problems, always locate centres first to exploit geometry.