A Pre-RMO question! -28

Geometry Level 4

Let line AC\overline{AC} be perpendicular to line CE\overline{CE}. Connect AA to the mid-point of CE\overline{CE} which is D,D, and connect EE to the mid-point of AC\overline{AC} which is BB.

If AD\overline{AD} and EB\overline{EB} intersect at point FF, BC=CD=15cm\overline{BC}=\overline{CD}=15cm, and area of DFE\triangle DFE is x cm2x\space cm^2 find xx.

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