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
Školjka