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anglechasing candidate, <EKF =?, when AK= EF, inside a square

Source: Estonia IMO TST 2007 p4

March 28, 2020
Angle Chasinganglessquaregeometry

Problem Statement

In square ABCD,ABCD, points EE and FF are chosen in the interior of sides BCBC and CDCD, respectively. The line drawn from FF perpendicular to AEAE passes through the intersection point GG of AEAE and diagonal BDBD. A point KK is chosen on FGFG such that ∣AK∣=∣EF∣|AK|= |EF|. Find ∠EKF.\angle EKF.
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