# Difference between revisions of "2006 Romanian NMO Problems/Grade 7/Problem 1"

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Let <math>ABC</math> be a triangle and the points <math>M</math> and <math>N</math> on the sides <math>AB</math> respectively <math>BC</math>, such that <math>2 \cdot \frac{CN}{BC} = \frac{AM}{AB}</math>. Let <math>P</math> be a point on the line <math>AC</math>. Prove that the lines <math>MN</math> and <math>NP</math> are perpendicular if and only if <math>PN</math> is the interior angle bisector of <math>\angle MPC</math>. | Let <math>ABC</math> be a triangle and the points <math>M</math> and <math>N</math> on the sides <math>AB</math> respectively <math>BC</math>, such that <math>2 \cdot \frac{CN}{BC} = \frac{AM}{AB}</math>. Let <math>P</math> be a point on the line <math>AC</math>. Prove that the lines <math>MN</math> and <math>NP</math> are perpendicular if and only if <math>PN</math> is the interior angle bisector of <math>\angle MPC</math>. | ||

==Solution== | ==Solution== | ||

+ | {{solution}} | ||

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==See also== | ==See also== | ||

*[[2006 Romanian NMO Problems]] | *[[2006 Romanian NMO Problems]] | ||

[[Category:Olympiad Geometry Problems]] | [[Category:Olympiad Geometry Problems]] |

## Revision as of 07:33, 27 August 2008

## 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

*This problem needs a solution. If you have a solution for it, please help us out by adding it.*