Question 25
Let $AD$ be the bisector of $\angle A$ of the triangle $ABC$. Let $M$ and $N$ be points on $AB$ and $AC$, respectively such that $\angle MDA=\angle ABC$ and $\angle NDA=\angle ACB$. Let $P$ be the intersection between $AD$ and $MN$. Suppose $AD=14$ cm. Find the value of $AB\times AC\times AP$ in cm$^3$.