IMO Shortlist 1988 problem 17
Dodao/la:
arhiva2. travnja 2012. In the convex pentagon
![ABCDE,](/media/m/3/e/c/3ec1b283a93da5b9331717859f65c68c.png)
the sides
![BC, CD, DE](/media/m/4/4/2/4426cba1d291a1e34fb125e661666c38.png)
are equal. Moreover each diagonal of the pentagon is parallel to a side (
![AC](/media/m/6/4/7/647ef3a5d68f07d59d84afe03a9dc655.png)
is parallel to
![DE](/media/m/a/c/d/acdf3f4d3c794d9a897484e9d216f5ec.png)
,
![BD](/media/m/1/1/f/11f65a804e5c922ee28a53b1df04d138.png)
is parallel to
![AE](/media/m/c/e/3/ce31f42a92358c211bccb23e6a92fb55.png)
etc.). Prove that
![ABCDE](/media/m/2/7/c/27c16cf5bf2e8ca59b13c61cf1562251.png)
is a regular pentagon.
%V0
In the convex pentagon $ABCDE,$ the sides $BC, CD, DE$ are equal. Moreover each diagonal of the pentagon is parallel to a side ($AC$ is parallel to $DE$, $BD$ is parallel to $AE$ etc.). Prove that $ABCDE$ is a regular pentagon.
Izvor: Međunarodna matematička olimpijada, shortlist 1988