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EF = AE + FC, square related (2008 Romania District VII P2)

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May 18, 2020
geometrysquareperpendicular

Problem Statement

Consider the square ABCDABCD and Eāˆˆ(AB)E \in (AB). The diagonal ACAC intersects the segment [DE][DE] at point PP. The perpendicular taken from point PP on DEDE intersects the side BCBC at point FF. Prove that EF=AE+FCEF = AE + FC.
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