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AM is a median of s triangle ABC. Is AB+...

`AM` is a median of s triangle `ABC.` Is `AB+BC+CA > 2AM?` (Consider the sides of triangles `DeltaABM and DeltaAMC.`

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To determine whether \( AB + BC + CA > 2AM \) holds true, we will analyze the triangle \( ABC \) and its median \( AM \). ### Step-by-Step Solution: 1. **Understanding the Median**: - The median \( AM \) of triangle \( ABC \) connects vertex \( A \) to the midpoint \( M \) of side \( BC \). By definition, \( BM = MC \). 2. **Applying the Triangle Inequality**: ...
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