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    OlympiadMediumProofs7–9

    Geometric Construction

    Construção Geométrica

    In triangle ABC, M is the midpoint of BC. Prove that AM≤AB+AC2AM \le \frac{AB + AC}{2}.

    Extend AM to point D such that MD=AMMD = AM. Then ABDC forms a parallelogram.

    Solution

    Step 1 of 8

    1. 1.Extend AM beyond M to D where MD=AMMD = AM.