78. In triangle $ABC$, the median $AM$ (the segment connecting vertex $A$ to the midpoint $M$ of side $BC$) is extended beyond point $M$ by a distance equal to $AM$. Find the distance from the resulting point to points $B$ and $C$, if sides $AB$ and $AC$ are equal to 5 and 4, respectively.
$\triangle$ Let $N$ be the end of the extended median, so that $N$ lies on the extension of $A M$ beyond point $M$ and $A M=M N$. Then, in the quadrilateral $A B N C$, the diagonals are bisected by their point of intersection, so we can refer to an already solved problem and see that the opposite sides of the quadrilateral are equal, that is, $N B=A C=4$, $N C=A B=5 . \triangleleft$