Question 4
(ARM) Let $M$ and $N$ be points inside triangle $ABC$ such that
$$\angle MAB=\angle NAC\qquad\angle MBA=\angle NBC.$$
Prove that
$$\frac{AM\cdot AN}{AB\cdot AC}+\frac{BM\cdot BN}{BA\cdot BC}+\frac{CM\cdot CN}{CA\cdot CB}=1.$$
$$\angle MAB=\angle NAC\qquad\angle MBA=\angle NBC.$$
Prove that
$$\frac{AM\cdot AN}{AB\cdot AC}+\frac{BM\cdot BN}{BA\cdot BC}+\frac{CM\cdot CN}{CA\cdot CB}=1.$$