In triangle $ABC$, $BC = 8$.  The length of median $AD$ is 5.  Let $M$ be the largest possible value of $AB^2 + AC^2$, and let $m$ be the smallest possible value.  Find $M - m$.
Question:
In triangle $ABC$, $BC = 8$.  The length of median $AD$ is 5.  Let $M$ be the largest possible value of $AB^2 + AC^2$, and let $m$ be the smallest possible value.  Find $M - m$.
Answer:
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In triangle $ABC$, $BC = 8$.  The length of median $AD$ is 5.  Let $M$ be the largest possible value of $AB^2 + AC^2$, and let $m$ be the smallest possible value.  Find $M - m$.
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