A Max Distance from a Median Condition

★ 7/10plane geometry Extrema conic sections AM-GM

Problem

In $\triangle ABC$ , $AM$ is the median to side $BC$ (with $M$ on $BC$ ), satisfying $AM=AB-AC$ , and $BC=4$ . Find the maximum distance from $A$ to the line $BC$ .

Answer

Solution

Difficulty	7/10
Topics	plane geometry, Extrema, conic sections, AM-GM

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