IMO Shortlist 1998 problem G7
Dodao/la:
arhiva2. travnja 2012. Let
![ABC](/media/m/a/c/7/ac75dca5ddb22ad70f492e2e0a153f95.png)
be a triangle such that
![\angle ACB=2\angle ABC](/media/m/f/e/a/feafa772087a87007fc03de875f353af.png)
. Let
![D](/media/m/7/0/0/7006c4b57335ab717f8f20960577a9ef.png)
be the point on the side
![BC](/media/m/5/0/0/5005d4d5eac1b420fbabb76c83fc63ad.png)
such that
![CD=2BD](/media/m/9/a/d/9ad899d128472fa55b4199e2524fcae7.png)
. The segment
![AD](/media/m/6/9/6/69672822808d046d0e94ab2fa7f2dc80.png)
is extended to
![E](/media/m/8/b/0/8b01e755d2253cb9a52f9e451d89ec11.png)
so that
![AD=DE](/media/m/7/6/8/7682f6228be04ed3ac684b5c0170328a.png)
. Prove that
commentEdited by Orl.
%V0
Let $ABC$ be a triangle such that $\angle ACB=2\angle ABC$. Let $D$ be the point on the side $BC$ such that $CD=2BD$. The segment $AD$ is extended to $E$ so that $AD=DE$. Prove that
$$\angle ECB+180^{\circ }=2\angle EBC.$$
commentEdited by Orl.
Izvor: Međunarodna matematička olimpijada, shortlist 1998