IMO Shortlist 2008 problem G4
Dodao/la:
arhiva2. travnja 2012. In an acute triangle
segments
and
are altitudes. Two circles passing through the point
anf
and tangent to the line
at the points
and
so that
lies between
and
. Prove that lines
and
intersect on the circumcircle of triangle
.
Proposed by Davood Vakili, Iran
%V0
In an acute triangle $ABC$ segments $BE$ and $CF$ are altitudes. Two circles passing through the point $A$ anf $F$ and tangent to the line $BC$ at the points $P$ and $Q$ so that $B$ lies between $C$ and $Q$. Prove that lines $PE$ and $QF$ intersect on the circumcircle of triangle $AEF$.
Proposed by Davood Vakili, Iran
Izvor: Međunarodna matematička olimpijada, shortlist 2008
Školjka 
