Difference between revisions of "2006 Romanian NMO Problems/Grade 7/Problem 1"
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| + | ==Problem== | ||
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== | ||
| + | ==See also== | ||
| + | *[2006 Romanian NMO Problems] | ||
Revision as of 10:16, 27 July 2006
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
See also
- [2006 Romanian NMO Problems]
