IMO Shortlist 2007 problem G3
Dodao/la:
arhiva2. travnja 2012. The diagonals of a trapezoid
![ABCD](/media/m/9/c/e/9ce25711ba18d9663b73c3580de4bf5a.png)
intersect at point
![P](/media/m/9/6/8/968d210d037e7e95372de185e8fb8759.png)
. Point
![Q](/media/m/4/5/c/45ce8d14aa1eb54f755fd8e332280abd.png)
lies between the parallel lines
![BC](/media/m/5/0/0/5005d4d5eac1b420fbabb76c83fc63ad.png)
and
![AD](/media/m/6/9/6/69672822808d046d0e94ab2fa7f2dc80.png)
such that
![\angle AQD = \angle CQB](/media/m/8/2/c/82c59647343aeb17a92bc326b8ede77a.png)
, and line
![CD](/media/m/8/9/5/895081147290365ccae028796608097d.png)
separates points
![P](/media/m/9/6/8/968d210d037e7e95372de185e8fb8759.png)
and
![Q](/media/m/4/5/c/45ce8d14aa1eb54f755fd8e332280abd.png)
. Prove that
![\angle BQP = \angle DAQ](/media/m/5/3/9/53975100e4618c1f74c6acf3e7ed4f08.png)
.
Author: unknown author, Ukraine
%V0
The diagonals of a trapezoid $ABCD$ intersect at point $P$. Point $Q$ lies between the parallel lines $BC$ and $AD$ such that $\angle AQD = \angle CQB$, and line $CD$ separates points $P$ and $Q$. Prove that $\angle BQP = \angle DAQ$.
Author: unknown author, Ukraine
Izvor: Međunarodna matematička olimpijada, shortlist 2007