MathNet 2024-part-01 — 168 problems (EN–VI) Question 149

Let $ABC$ be a triangle with side lengths $AB = 13$, $BC = 14$, $CA = 15$. Let $A'B'C'$ be a translate of $ABC$ by some unit vector. Find the largest possible area of the intersection of triangles $ABC$ and $A'B'C'$.