Here let A, B, C, and D be four distinct points in the plane. Now supposedly that no three of them lie on a line and A, C are on opposite sides of the line BD. Now the lengths of the line segments AB, BC, CD and DA are 4, 3, 6 and 8 respectively. (a) What is the range of possible values for the length x of the line segment BD? (Justify your answer) (b) Now suppose that x = 7. What is the length of the line segment AC?

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