MathNet 2018-part-04 — 181 problems (EN–VI) Question 2

In triangle $ABC$, $AB = 6$, $BC = 10$, and $CA = 14$. If $D$, $E$, and $F$ are the midpoints of sides $BC$, $CA$, and $AB$, respectively, find $AD^{2} + BE^{2} + CF^{2}$.