IMO Shortlist 2001 problem G8
Dodao/la:
arhiva2. travnja 2012. Let
![ABC](/media/m/a/c/7/ac75dca5ddb22ad70f492e2e0a153f95.png)
be a triangle with
![\angle BAC = 60^{\circ}](/media/m/c/4/8/c48394dd0aa64809e94e38140750c8e3.png)
. Let
![AP](/media/m/7/b/0/7b05fe3b464ec24a15fa5701f4d14b61.png)
bisect
![\angle BAC](/media/m/b/2/1/b21a9e466104c5d33646432221e142be.png)
and let
![BQ](/media/m/2/8/c/28cc5d89f53243e9e0fb41492df4736b.png)
bisect
![\angle ABC](/media/m/c/9/2/c92dca0f4ca20d0ca087b59e09a26fa8.png)
, with
![P](/media/m/9/6/8/968d210d037e7e95372de185e8fb8759.png)
on
![BC](/media/m/5/0/0/5005d4d5eac1b420fbabb76c83fc63ad.png)
and
![Q](/media/m/4/5/c/45ce8d14aa1eb54f755fd8e332280abd.png)
on
![AC](/media/m/6/4/7/647ef3a5d68f07d59d84afe03a9dc655.png)
. If
![AB + BP = AQ + QB](/media/m/f/3/7/f378e9dedabd8b29014bf92d3fbf031c.png)
, what are the angles of the triangle?
%V0
Let $ABC$ be a triangle with $\angle BAC = 60^{\circ}$. Let $AP$ bisect $\angle BAC$ and let $BQ$ bisect $\angle ABC$, with $P$ on $BC$ and $Q$ on $AC$. If $AB + BP = AQ + QB$, what are the angles of the triangle?
Izvor: Međunarodna matematička olimpijada, shortlist 2001