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 \(FGHJ\).

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