# 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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