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FD _|_ BE wanted, hexagon ABCDE, AB = BC, CD = DE, EF = FA, <A=<C=90^o

Source: 2005 Oral Moscow Geometry Olympiad grades 8-9 p4

October 16, 2020
geometryperpendicularhexagonequal segmentsright angle

Problem Statement

Given a hexagon ABCDEFABCDEF, in which AB=BC,CD=DE,EF=FAAB = BC, CD = DE, EF = FA, and angles AA and CC are right. Prove that lines FDFD and BEBE are perpendicular.
(B. Kukushkin)
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