Question 85
Let $ABCD$ be a parallelogram such that the bisector from $B$ meets side $CD$ at its midpoint $M$. Side $BC$ has length $6$, and diagonal $AC$ has length $14$. Determine the length of $AM$.
(A) $2 \sqrt{19}$
(B) $14-3 \sqrt{3}$
(C) $4 \sqrt{5}$
(D) $9$
(E) $2 \sqrt{22}$
(A) $2 \sqrt{19}$
(B) $14-3 \sqrt{3}$
(C) $4 \sqrt{5}$
(D) $9$
(E) $2 \sqrt{22}$