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isosceles AB=AC, BF=BE, angle bisector, BD=EF iff AF=EC 2016 Dutch IMO TST2 P3

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August 4, 2019
geometryequal segmentsisoscelesangle bisector

Problem Statement

Let △ABC\vartriangle ABC be an isosceles triangle with ∣AB∣=∣AC∣|AB| = |AC|. Let D,ED, E and FF be points on line segments BC,CABC, CA and ABAB, respectively, such that ∣BF∣=∣BE∣|BF| = |BE| and such that EDED is the internal angle bisector of ∠BEC\angle BEC. Prove that ∣BD∣=∣EF∣|BD|= |EF| if and only if ∣AF∣=∣EC∣|AF| = |EC|.
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