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Explanation

Once again we take advantage of the fact that the y-coordinates of A and B are the same.
Thus AB is parallel to x-axis, its equation being y = 4. The mid-point of AB is M(1, 4)
Let S be the centre of the circle. Then SM is perpendicular to AB

Since AB is parallel to x-axis, Ms is parallel to y. Thus x-coordinate of S is 1.
Again S lies on 4y = x + 7, `therefore` y-coordinate of S is 2. We get
MS = 2 `therefore` BC = 2MS = 4
AB = 8
Area of rectangle AB. CD = AB.BC = (8)(4) = 32 square units.