Question 97
On the sides $BC$, $CA$ and $AB$ of triangle $ABC$, respectively, points $D$, $E$ and $F$ are chosen. Prove that
$$
\frac{1}{2} (BC + CA + AB) \lt AD + BE + CF \lt \frac{3}{2} (BC + CA + AB).
$$
$$
\frac{1}{2} (BC + CA + AB) \lt AD + BE + CF \lt \frac{3}{2} (BC + CA + AB).
$$