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Non-stanard easy geo inequality [Serbia TST 2017, D1, P1]

Source: Serbia TST 2017, Day 1, Problem 1

May 21, 2017

inequalitiesgeometry

Problem Statement

Let

ABC

be a triangle and

D

the midpoint of the side

BC

. Define points

E

and

F

AC

and

B

, respectively, such that

DE=DF

and

\angle EDF =\angle BAC

. Prove that

DE\geq \frac {AB+AC} 4.