IMO Shortlist 1998 problem G4
Dodao/la:
arhiva2. travnja 2012. Let
![M](/media/m/f/7/f/f7f312cf6ba459a332de8db3b8f906c4.png)
and
![N](/media/m/f/1/9/f19700f291b1f2255b011c11d686a4cd.png)
be two points inside triangle
![ABC](/media/m/a/c/7/ac75dca5ddb22ad70f492e2e0a153f95.png)
such that
Prove that
%V0
Let $M$ and $N$ be two points inside triangle $ABC$ such that
$$\angle MAB = \angle NAC\quad \mbox{and}\quad \angle MBA = \angle NBC.$$
Prove that
$$\frac {AM \cdot AN}{AB \cdot AC} + \frac {BM \cdot BN}{BA \cdot BC} + \frac {CM \cdot CN}{CA \cdot CB} = 1.$$
Izvor: Međunarodna matematička olimpijada, shortlist 1998