Given a cyclic quadrilateral
, let
be the midpoint of the side
, and let
be a point on the circumcircle of triangle
. Assume that the point
is different from the point
and satisfies
. Prove that the points
,
,
are collinear, where
and
.
%V0
Given a cyclic quadrilateral $ABCD$, let $M$ be the midpoint of the side $CD$, and let $N$ be a point on the circumcircle of triangle $ABM$. Assume that the point $N$ is different from the point $M$ and satisfies $\frac{AN}{BN}=\frac{AM}{BM}$. Prove that the points $E$, $F$, $N$ are collinear, where $E=AC\cap BD$ and $F=BC\cap DA$.
Školjka