# 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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