# AIME Problem 4

Geometry Level 4

In the diagram below, $$ABCD$$ is a square. Point $$E$$ is the midpoint of $$\overline{AD}$$. Points $$F$$ and $$G$$ lie on $$\overline{CE}$$, and $$H$$ and $$J$$ lie on $$\overline{AB}$$ and $$\overline{BC}$$, respectively, so that $$FGHJ$$ is a square. Points $$K$$ and $$L$$ lie on $$\overline{GH}$$, and $$M$$ and $$N$$ lie on $$\overline{AD}$$ and $$\overline{AB}$$, respectively, so that $$KLMN$$ is a square. The area of $$KLMN$$ is 99. Find the area of $$FGHJ$$.

This problem is part of this set.

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