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Balkan geo 2000

Source: balkan mathematical olympiads 2000

April 7, 2006

geometry solvedgeometry

Problem Statement

Let

N

be an acute-angled triangle and

D

the midpoint of

BC

. Let

E

be a point on segment

AD

and

M

its projection on

BC

. If

N

and

P

are the projections of

M

on

AB

and

AC

then the interior angule bisectors of

\angle NMP

and

\angle NEP

are parallel.

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