MEMO 2010 pojedinačno problem 3
Dodao/la: arhivaApril 28, 2012
We are given a cyclic quadrilateral
with a point
on the diagonal
be the center of the circumcircle
of the triangle
. The circle
intersects the line
in the points
. Prove that the lines
meet at one point.
We are given a cyclic quadrilateral $ABCD$ with a point $E$ on the diagonal $AC$ such that $AD=AE$ and $CB=CE$. Let $M$ be the center of the circumcircle $k$ of the triangle $BDE$. The circle $k$ intersects the line $AC$ in the points $E$ and $F$. Prove that the lines $FM$, $AD$ and $BC$ meet at one point.
Source: Srednjoeuropska matematička olimpijada 2010, pojedinačno natjecanje, problem 3