Euler's quadrilateral theorem states that for any convex quadrilateral, the sum of the lengths of the opposite sides is equal if and only if the quadrilateral is cyclic. A cyclic quadrilateral is one that can be inscribed in a circle, meaning all its vertices lie on the circumference of that circle. To put it more formally, for a convex quadrilateral \(ABCD\), if \(AB + CD = AD + BC\), then the quadrilateral \(ABCD\) is cyclic.

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