MEMO 2011 ekipno problem 5
Dodao/la:
arhiva28. travnja 2012. Let
![ABCDE](/media/m/2/7/c/27c16cf5bf2e8ca59b13c61cf1562251.png)
be a convex pentagon with all five sides equal in length. The diagonals
![AD](/media/m/6/9/6/69672822808d046d0e94ab2fa7f2dc80.png)
and
![EC](/media/m/4/e/4/4e4170b0db307c7c97263f5efe9ebc41.png)
meet in
![S](/media/m/c/6/3/c63593c3ec0773fa38c2659e08119a75.png)
with
![\angle ASE = 60^\circ](/media/m/b/a/3/ba3c7ff7cdab35f1ae091acb53a66041.png)
. Prove that
![ABCDE](/media/m/2/7/c/27c16cf5bf2e8ca59b13c61cf1562251.png)
has a pair of parallel sides.
%V0
Let $ABCDE$ be a convex pentagon with all five sides equal in length. The diagonals $AD$ and $EC$ meet in $S$ with $\angle ASE = 60^\circ$. Prove that $ABCDE$ has a pair of parallel sides.
Izvor: Srednjoeuropska matematička olimpijada 2011, ekipno natjecanje, problem 5