Question 63
$ABC$ is a triangle with integral sides. $M$ is the midpoint of $BC$. The in-circle with centre $I$ touches $AB$ and $AC$ at $E$ and $F$ respectively and $D$ is the projection of $M$ on $EF$. Suppose that $ADMI$ is a parallelogram and $AB + BC + CA = 65$. Find $AB \times BC \times CA$.