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2006 Romanian NMO Problems/Grade 7/Problem 1

Revision as of 07:33, 27 August 2008 by 1=2 (talk | contribs) (when a problem doesn't have a solution, put a {{solution}} tag under it if there isn't already.)

Problem

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

Solution

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See also

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