Question 4
(SPA 2) In the triangle $ABC$, let $D,E$ be points on the side $BC$ such that $\angle BAD=\angle CAE$. If $M,N$ are, respectively, the points of tangency with $BC$ of the incircles of the triangles $ABD$ and $ACE$, show that
$$\frac1{MB}+\frac1{MD}=\frac1{NC}+\frac1{NE}.$$
$$\frac1{MB}+\frac1{MD}=\frac1{NC}+\frac1{NE}.$$