Question 82
Let $\triangle ABC$ be a triangle and let $P$ denote the midpoint of the side $BC$. Suppose that there exist two points $M$ and $N$ interior to the sides $AB$ and $AC$ respectively, such that
$$
|AD| = |DM| = 2|DN|,
$$
where $D$ is the intersection point of the lines $MN$ and $AP$. Show that
$|AC| = |BC|$.
$$
|AD| = |DM| = 2|DN|,
$$
where $D$ is the intersection point of the lines $MN$ and $AP$. Show that
$|AC| = |BC|$.