2015 AIME I Problems/Problem 7
7. In the diagram below, is a square. Point is the midpoint of . Points and lie on , and and lie on and , respectively, so that is a square. Points and lie on , and and lie on and , respectively, so that is a square. The area of is 99. Find the area of .
We begin by denoting the length , giving us and . Since angles and are complimentary, we have that $\triangle CDE \~ \triangle JFC$ (Error compiling LaTeX. ! Missing $ inserted.) (and similarly the rest of the triangles are triangles). We let the sidelength of be , giving us:
Solving for in terms of yields .
We now use the given that , implying that . We also draw the perpendicular from E to ML and label the point of intersection P:
This gives that and
Since = , we get
So our final answer is
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