MathDB

3

Part of 2016 Grand Duchy of Lithuania

Problems(1)

BD = EF iff AF = EC, ABC isosceles, BF = BE,ED is angle bisector of <BEC

Source: 2016 Grand Duchy of Lithuania, Mathematical Contest p3 (Baltic Way TST)

10/3/2020
Let ABCABC be an isosceles triangle with AB=ACAB = AC. Let D,ED, E and FF be points on line segments BC,CABC, CA and ABAB, respectively, such that BF=BEBF = BE and such that EDED is the angle bisector of ∠BEC\angle BEC. Prove that BD=EFBD = EF if and only if AF=ECAF = EC.
geometryequal segmentsisosceles