$17 \cdot 32$ In an acute triangle $\triangle ABC$, the angle bisector of $\angle A$ intersects side $BC$ at $D$. A circle with center $B$ and radius $BD$ intersects side $AB$ at $M$; a circle with center $C$ and radius $CD$ intersects side $AC$ at $N$. The statement that is always true is
(A) $\angle CND + \angle BMD - \angle DAC = 120^{\circ}$.
(B) $AMDN$ is a trapezoid.
(C) $BC$ is parallel to $MN$.
(D) $AM - AN = \frac{3(DB - DC)}{2}$.
(E) $AB - AC = \frac{3(DB - DC)}{2}$.
(26th American High School Mathematics Examination, 1975)