# 2006 Romanian NMO Problems/Grade 7/Problem 1

## Problem

Let be a triangle and the points and on the sides respectively , such that . Let be a point on the line . Prove that the lines and are perpendicular if and only if is the interior angle bisector of .

## Solution

Let be a point on such that is the midpoint of , then =, the given information is the same as \frac{LN}{BC} = \frac{AM}{AB}MLAC$.

Let$ (Error compiling LaTeX. ! Missing $ inserted.)RMNMNNRMNNRLNNCRLMCCRMLMLACACRMNPNNPMCPN\angle MPRPN\angle MPC$, as requiered.