IMO Shortlist 2006 problem G3
Dodao/la:
arhiva2. travnja 2012. Consider a convex pentagon
![ABCDE](/media/m/2/7/c/27c16cf5bf2e8ca59b13c61cf1562251.png)
such that
Let
![P](/media/m/9/6/8/968d210d037e7e95372de185e8fb8759.png)
be the point of intersection of the lines
![BD](/media/m/1/1/f/11f65a804e5c922ee28a53b1df04d138.png)
and
![CE](/media/m/3/3/7/33771853199c7fd8dc7faa2d4a37425d.png)
. Prove that the line
![AP](/media/m/7/b/0/7b05fe3b464ec24a15fa5701f4d14b61.png)
passes through the midpoint of the side
![CD](/media/m/8/9/5/895081147290365ccae028796608097d.png)
.
%V0
Consider a convex pentagon $ABCDE$ such that
$$\angle BAC = \angle CAD = \angle DAE\ \ \ ,\ \ \ \angle ABC = \angle ACD = \angle ADE$$
Let $P$ be the point of intersection of the lines $BD$ and $CE$. Prove that the line $AP$ passes through the midpoint of the side $CD$.
Izvor: Međunarodna matematička olimpijada, shortlist 2006