IMO 1974 LL USS46

Origin: USS

Problem

Outside an arbitrary triangle ABC, triangles ADB and BCE are constructed such that \angleADB = \angleBEC = 90◦and \angleDAB = \angleEBC = 30◦. On the segment AC the point F with AF = 3FC is chosen. Prove that \angleDFE = 90◦ and \angleFDE = 30◦.