Can you find all such quadrilaterals?

Geometry Level pending

Let \(ABCD \) be a convex quadrilateral where \(E,F,G,H\) are the midpoints of \(AB,BC,BD,DA\) respectively.

If \(AB+CD=2EG\)

\(BC+DA=2FH\)

define \(k =\) \(\frac{area \space of \space ABCD}{AB^2+BC^2+CD^2+DA^2}\).

Then which of the following is true regading \(ABCD\).

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