Question 83
Let $ABC$ be an equilateral triangle and let $D$ be an interior point of side $BC$. Let a circle touch $BC$ in $D$ and divide the sides $AB$ and $AC$ in the inner points $M, N$ and $P, Q$. Prove that is true
$$
|BD| + |AM| + |AN| = |CD| + |AP| + |AQ|
$$
$$
|BD| + |AM| + |AN| = |CD| + |AP| + |AQ|
$$