Product Of Opposite Sides In A Quadrilateral

Geometry Level 5

Let \(ABCD\) be a convex quadrilateral such that \(AB\cdot CD=12\), \(BC\cdot AD=14\) and \(\cos (\angle A+\angle C)=-\frac{2}{3}\). Find the value of \((BD\cdot AC)^2 \).

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