Question 35
Let $ABC$ be a triangle in the plane with $AB = 13$, $BC = 14$, $AC = 15$. Let $M_n$ denote the smallest possible value of $\left(AP^n + BP^n + CP^n\right)^{\frac{1}{n}}$ over all points $P$ in the plane. Find $\lim_{n \rightarrow \infty} M_n$.