Apply Midpoint Theorem?

Geometry Level 5

Let \(ABCD\) be a convex quadrilateral, and let the midpoints of \(AB\), \(BC\), \(CD\) and \(DA\) be \(K\), \(L\), \(M\) and \(N\). Let \(KM\) intersect \(LN\) at \(T\). If the area of \(BKTL\) is 15, find the sum of the infimum and the supremum areas of \(ABCD\).

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