A Parallel Segment Inequality

★ 7/10plane geometry Law of Cosines Completing the Square AM-GM inequality vectors

Problem

In $\triangle ABC$ , $A = 120^\circ$ and $D$ is the midpoint of side $BC$ . Points $E, F$ move along sides $AB, AC$ respectively with $EF \parallel BC$ . Prove that

DE + DF \geqslant BD.

Answer

Solution

Difficulty	7/10
Topics	plane geometry, Law of Cosines, Completing the Square, AM-GM, inequality, vectors

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